Is Billy Breckenridge gay?

Possibly

It must be recalled that what "evidence" we have is based on written accounts which, it must be stated, are not unbiased.

My googling has unearthed the 'fact' that it was rumoured for a long time that Breakenridge, who never married, was homosexual. This appears to be based on one or more books written after his death.

These rumours may have been spread by, amongst others, Wyatt Earp's wife, Josephine.

...There was probably no occupation in the West that did not have lesbian and gay participants. William Breakenridge had worked as a Union Pacific brakeman and joined the Third Colorado Cavalry before becoming a deputy sheriff at Phoenix and then Tombstone, Arizona Territory in 1881, where he was known to, and accepted by many of the mining town's community. He was later appointed Deputy U.S. Marshall and finally a special detective for the Southern Pacific railroad. After Breakenridge's retirement, former Wells, Fargo & Co. detective Fred Dodge joked that "Billy was a nice young girl in those days, and undoubtedly today is a nice old lady." Josephine Earp, who with her husband Wyatt knew Breakenridge for many years, later declared that "the one thing I can say in his favor is that he avoided the liaisons with the dance-hall women who so enamored his associates."

^{Homosexuality in the American West}

However, it should be noted that Earp and his wife were not fans of Breakenridge who was considered to be anti-Earp during the Tombstone days.

In 1928, he [Breakenridge] became a published author with the release of his memoirs of life in Tombstone and the old west, Helldorado: Bringing the Law to the Mesquite. Critics of the book, including Wyatt Earp and his wife Josie, claimed that much of what Breakenridge wrote was biased and more fiction than factual. Although Breakenridge met with Earp in Los Angeles to interview him, the picture he painted of Earp was less than flattering.

^Wikipedia

One can only conclude that, although not essential to the plot, the films writers/creators considered it accurate enough to have Priestly portray Breakenridge as he did.

To understand the homosexual representation by Jason Priestly in "Tombstone" well I think one must grasp that a couple of years before Wyatt Earp died in Los Angeles, an embittered old man at the poor treatment he thought himself to have received in Breckenridge's own biography, "Helldorado" complaining to his own working biographer, Stuart Lake, that "Helldorado" was a kind of torpedo job, full of character assassination calling the Earp faction in Tombstone "The Earp Gang" Lake promised Earp, just before he died, that he, Lake, would set the record straight, and you can tell in watching the 1993 MOVIE Tombstone" that the writers of that script had totally bought into the Earp version, Based itself upon Lake's far famed "Wyatt Earp -- frontier Marshall" that proved the bedrock of nearly all Earp/Doc Holliday movies since declaring the "cowboys" nothing better than one of the first waves of American organized crime, casting in very dark light such figures as Curly Bill Brocius and Johnny Ringo, both friends of Breckenridge, and I do believe he, Breckenridge, was portrayed unflatteringly as "Sisterboy", an appelation borrowed from that old fifties movie, "Tea and Sympathy" and connected this gay slur with Breckenridge as a kind of insider joke, as in he who laughs last laughs best. Otherwise, I know of no evidence that Breckenridge was actually gay. "Helldorado" BTW also supplied the model for "Tombstone's" Curly Bill, so beautifully played by Powers Booth, and I URGE OTHERS TO READ "helldorado" if for no other reason to see how clearly Booth leaned on "Helldorado" for his hilarious portrayal of the chief Cowboy badasser, an anecdote from which book appears so oddly in the old Western series, "Tombstone Territory" where fictional Tombstone sheriff, Clay Hollister, is dead set on deputizing Curly Bill as an assistant tax collector of the Cowboys' illicet riches, which is JUST what Breckenridge said he himself did in "Heldorado"...read this book -- it is a must read.