People are “more memorable if they leave you a big tip or not a tip at all instead of a normal tip,” Ms. Starks said. “Of all the people Cameron served that night, it just so happened that these were the only people to not leave him a tip at all.”

The men in the bar video were the same ones who lit the Christmas tree, Ms. Starks and the police said. They left the bar around 1:50 a.m. on New Year’s Day, and the Southernmost Point Buoy fire occurred around 3:20 a.m., the police said.

The police identified the duo as Skylar Rae Jacobson, 21, of Texas, and David Brendan Perkins, 22, of Leesburg, Fla. The police said they had obtained felony arrest warrants for both men on suspicion of criminal mischief with more than $1,000 in damage. The two men did not respond to requests for comment by phone and text message.

According to the police report, the men confessed over the phone when reached by an investigator. Mr. Perkins said that the men had found the tree on Duval Street around 2:30 or 3 a.m. and that they had no intention of damaging property, according to the report. They used a lighter to start the fire and did not add any fuel, the report states. Mr. Perkins called it “a colossal mistake,” the report said, while Mr. Jacobson said they “weren’t thinking.”

The Conch Republic, the name adopted in the city’s tongue-in-cheek 1982 secession from Florida that has turned into the city’s playful alter ego, is forgiving. Some of its denizens, like Jim Gilleran, a boat captain and bar owner who calls himself the republic’s secretary of state, don’t want the pair to do jail time.

“The secretary of state doesn’t think these folks should be punished,” the secretary of state said. “They should serve community service so they really can appreciate what a great community we have here.”