In a glowing underpass in Central Park one night last month, a man and woman danced through a boxing routine. They skipped rope and sparred. He swung and she ducked. Echoing through the space, playing on a cellphone, was a piano composition by the Cuban composer Ernesto Lecuona. It had the feel of a dirge, possibly because Fidel Castro had died three nights earlier.

“I still don’t want to accept it,” the trainer, Brin-Jonathan Butler, said. “A year after from now, no one will believe it all ever existed.”

Mr. Butler, 37, is among his generation’s foremost boxing writers — the candidate pool for his anachronistic profession is admittedly small — and his book, “The Domino Diaries,” an immersion into Cuba’s boxing culture, positions him in a line of literary acolytes of Ernest Hemingway. But being a boxing writer now is a less viable career path than it was in Hemingway’s day, and the exotic Havana he visited is becoming a popular Instagram destination for JetBlue passengers.

So Mr. Butler makes ends meet by teaching boxing to a dozen or so clients at $90 a session in Central Park, no matter the weather. “When I came to New York, someone told me ‘You’re either rich or you have a second job,’” he said.

His book, which Picador published last year and recently came out in paperback, recounts his trip to Cuba in 2000 with little more than boxing gloves, a wad of cash and a vague plan to research Cuban boxing. He ended up living there on and off for a decade. His small apartment in an East Harlem walk-up is filled with tattered pictures of Che Guevara and Castro. “Some people have a feeling home is not where you were born,” he said. “I felt I’d come home when I went to Havana.”

For boxing fans, Cuba holds an outsize mystique. Since Castro took power in 1959, the island has won more Olympic gold medals in boxing than any other country, but its fighters have for the most part resisted the temptation to defect to the United States, turning down multimillion-dollar offers in apparent loyalty to the revolution. Mr. Butler found the paradox worth exploring, and his book argues that the sport is as entwined with Cuba’s narrative of defiance toward America as much as anything else.

His adventures over the years were plentiful. He interviewed Cuba’s most decorated boxers, finding them living in poverty: Several had sold their gold medals because they needed the money; another agreed to train him for $6 a day, and another decreed he chug a glass of vodka as a test of character. The book chronicles Mr. Butler’s fling with one of Castro’s granddaughters and the time he bet his life savings on a fight (he won). He also retraced Hemingway’s footsteps, talking his way into his literary idol’s home and traveling to a small fishing town to find the old man who inspired “The Old Man and the Sea,” who was then 102.

These days, you can find him in Central Park. Another tune started to play as his student agonized through push-ups. “You’d see these boxers dominate at the Olympics, and then they’d just disappear,” he said. “They were fighting for something more important than money. I had to go find out why.”

Mr. Butler was born in Vancouver, British Columbia, in 1979 and began boxing, he said, for the same reason everyone starts boxing. “When you get into the ring, you think everyone’s there for a different reason than you, but that’s not true,” he said. “It’s all the same reason: to reclaim respect.” In his case, classmates violently ambushed him on an empty field when he was 11. He retreated into reading Dostoyevsky and punching heavy bags.

He arrived in Havana when he was 20, around the time of the Elián González conflict. His book started writing itself on the plane. An antique bookseller seated beside him claimed to know the location of Gregorio Fuentes, the fisherman who inspired Hemingway; flight attendants had cut off the bookseller from more alcohol, however, and he agreed to help only if Mr. Butler ordered him more whiskey.

Soon after settling into Havana, Mr. Butler found himself knocking on a door in the quiet fishing village of Cojímar, east of the capital. He spent only 20 minutes with the wrinkled man who emerged. “He said that after Hemingway committed suicide, he never fished again,” Mr. Butler recalled. “He told me, ‘He was my friend, and I never wanted to fish again after that.’” Mr. Fuentes died two years later.

John Hemingway, one of Ernest Hemingway’s grandsons, became a fan of Mr. Butler’s writing and started a correspondence with him. “I really liked a piece he wrote about bullfighting in Spain, so I wrote him a letter,” Mr. Hemingway said in a phone call. “Brin looks at the corrida as the art form we consider it to be. We almost went to see José Tomás in Mexico City together. He’s the best bullfighter in the world right now. Anyone who gets the chance to see him before he retires or gets killed is in for a treat.”

But Mr. Butler spent most of his time in Cuba, living in a crumbling apartment on Neptune Street, exploring the thesis of his book. “Heroes weren’t for sale,” he wrote. “But how long could that last? How long could anyone resist not cashing in? And if no price was acceptable to sell out, what was the cost of that stance?”

He enlisted at Rafael Trejo, a historic boxing gym in the city’s old red-light district, where wrenches were banged against fire extinguishers as bells. “These old women guarded the door,” he said. “They reminded me of the sisters from ‘Macbeth.’ You had to pay them $2 to enter, but then you trained outside under the stars and punched tires instead of punching bags.”

Everything Mr. Butler thought he knew about boxing got turned backward: At government-funded stadium matches, there were no cameras, no concession stands, no corporate sponsorships, no ticket scalpers and no V.I.P. seating. There was also no air-conditioning.

“Without the incentive of money, I watched people fight harder than anywhere else I’d ever seen,” he wrote. “But I knew full well that most Cuban champions were so desperate for money that many had sold off all their Olympic medals, and even uniforms, to the highest tourist bidder. That part of the Cuban sports legacy was omitted from their tales.”

He found his first Olympian, Héctor Vinent, shortly after arriving. Mr. Vinent, who won Olympic gold medals in the 1990s, started training Mr. Butler at the gym for $6 a session. Mr. Butler then found Teófilo Stevenson, whom the BBC once described as Cuba’s “most famous figure after Fidel Castro.” Mr. Stevenson became a Cuban legend after winning three consecutive Olympic gold medals (’72, ’76, ’80) and turning down $5 million to fight Muhammad Ali in the United States. Tall and strapping, his refusal to defect made him a potent symbol of the revolution. When Mr. Butler found him, he was living in penury at 59, charging $130 to be interviewed on camera at his Havana home. He died a year later.

“He turned down millions to leave, and here was begging for $130 to talk about turning down millions,” Mr. Butler said. “He was the perfect canary in the coal mine because his situation reflected the health of the revolution.”

The cork board above Mr. Butler’s writing desk in Harlem. Credit Hilary Swift for The New York Times
The former champion was self-conscious of his living conditions, Mr. Butler said, and initially requested that the camera focus on a wall. He also made the unusual request, as it was 9 in the morning, that Mr. Butler consume a tall glass of vodka to establish trust. The conversation is believed to be the boxer’s last videotaped interview.

Mr. Butler also encountered Félix Savón and Guillermo Rigondeaux. Mr. Savón was similarly elevated to heroic status after winning three gold medals and refusing multimillion-dollar offers to fight Mike Tyson. He is said to have told the boxing promoter Don King, “What do I need $10 million for when I have 11 million Cubans behind me?” And when promoters came to his Havana home, Mr. Butler reported in his book, Mr. Savón’s wife boasted, “Félix is more revolutionary than Fidel.”

Mr. Rigondeaux, on the other hand, broke ranks while Mr. Butler was there, defecting to the United States in 2009. Indications of his rebelliousness, perhaps, were apparent when Mr. Butler encountered him: He claimed he had melted his two Olympic gold medals to wear as grills on his teeth. The Ring magazine now ranks him the No. 1 junior featherweight in the world.

Of course, Mr. Butler didn’t devote his every waking moment to studying Cuba’s sports system. At a New Year’s Eve party in 2006, he met one of Castro’s granddaughters. “She asked me for a cigarette,” he said. “She seemed impressed I didn’t care who she was.” In an unusual gesture of flirtation, she recited Castro’s personal phone number. A retelling of what followed was published on the sports website Deadspin with the cheeky headline: “The Time I Went to Havana and Hooked Up With Castro’s Granddaughter.”

He concluded his travels the same day Osama bin Laden was killed in 2011. Even as he headed to the airport, he said, the nation’s idiosyncrasies followed him. “No one in Cuba knew that he had been killed yet,” he said. “I only found out because I ran into a New Yorker who was yelling to everybody, ‘We got him!’ His hotel had a TV with an American news channel.”

In New York, a short-lived marriage ended in divorce. A documentary he made about his adventures left him $50,000 in debt (he has struggled to get the film released), and though “The Domino Diaries” received good reviews, it sold poorly. But Mr. Butler didn’t linger on the financial outcome of his travels. “J. D. Salinger said, ‘Write the book you want to read,’ and I got to do that,” he said. “Writing about Cuba was an honor.”

He prepped boxing gear at his East Harlem apartment before a lesson in Central Park last month. His library is cluttered with books by sportswriters like Jimmy Cannon and A. J. Liebling. A “private property” sign he said he pried off a tree from Salinger’s property hangs on a wall. The ticket to a fight at the Kid Chocolate Arena in Havana is pinned above his desk alongside a picture of a shirtless Castro doing a pull-up. His cat, Fidel, stared down from atop a pile of books.

Mr. Butler is aware that he writes about a sport that increasingly exists on the margins. “Fighters complain to me about boxing writers now,” he said. “‘You guys aren’t as good as you used to be.’ And I say, ‘There’s not the money there used to be.’” He continued, “‘I’m on Medicaid, I’m living below the poverty line, and I’m also in Vegas at the ring writing about your fight.’”

And in Manhattan, boxing is a lonely sport to love when even many of those he teaches cannot name the current heavyweight champion of the world. He is something of a holdout in that sense and has become a walking repository of the city’s boxiana.

The daughter of one the sport’s best writers, Mark Kram, is a student of Mr. Butler’s; his coffee companion and confidant, Thomas Hauser, is Ali’s official biographer; and he often passes Saturday evenings in the boxing-memorabilia-filled apartment of a widow in Hamilton Heights who tapes practically every televised fight. (“I can’t believe we paid $30 for that miserable pay-per-view out of Puerto Rico,” she lamented as she and Mr. Butler watched the recent Manny Pacquiao fight over wine and her homemade tacos.)

Mr. Butler calls his lessons “guerrilla style.” Of the trend of boxing as fitness for “Wall Street guys,” he said: “They do it to feel something. Anything. Boxing gyms are parks for rich people now. Black fighters are exotic as trainers to them. Gyms aren’t the lifelines they were to kids anymore.”

The gig is necessary to support his craft, he said, though he has written lengthy literary articles for publications like the The Paris Review, Esquire and ESPN the Magazine, and has been mentioned in the Best American Sports Writing anthology three times. He is working on a book about chess for Simon & Schuster. “I wrote well over a million words before I was paid for one,” he said.

“I’m having to struggle and grind like the fighters I write about,” he concluded. “That makes it easy for me to sympathize with them.”

But Mr. Butler tends to stay away from doom and gloom, focusing on the tale at hand. Indeed, he brightened at the park when he thought about Castro’s love for boxing. “He was a fanatic,” he said, starting to wind up another story: Félix Savón was battling the American boxer Shannon Briggs at the 1991 Pan-American Games. Castro was watching in the audience.

“Cuba is absolutely demolishing the U.S. in the ring,” Mr. Butler said. “Everyone in the stadium starts doing the wave and Fidel jumps up with them. Fidel Castro started doing the wave.”

A version of this article appears in print on December 18, 2016, on Page MB1 of the New York edition with the headline: The Trials of a Boxing Romantic.