The original meaning of the phrase transpires from the expression “seeing pink elephants," a euphemism for a drunken hallucination caused by delirium tremens. Describing one sort of alcoholic in the autobiographical John Barleycorn, Jack London writes that he "is the man whom we all know, stupid, unimaginative, whose brain is bitten numbly by numb maggots; who walks generously with wide-spread, tentative legs, falls frequently in the gutter, and who sees, in the extremity of his ecstasy, blue mice and pink elephants. He is the type that gives rise to the jokes in the funny papers."
A reference to pink elephants occurs in the 1941 Disney animated classic “Dumbo.” Having taken a drink of water from a bucket spiked with moonshine, Dumbo begins to hallucinate, singing and dancing "Pink Elephants on Parade."
Recently, “pink elephant" has come to serve as one version of "the elephant in the room" (something that everyone is aware of but won't speak of). This usage is only found occasionally.
Now we turn to the gay meaning. "Pink elephant" is also a jocular term for Log Cabin Republicans (LCR; gay Republicans). The symbol of the U.S. Republican party is the elephant, and pink suggests homosexuality (as in the pink triangle). The shade ranks as a stereotypically effeminate version of the color red, used to signify the party since 2000. The Foley affair turned the spotlight on gay staffers in Washington who work for Republican elected officials. Whether they are LCR members or not, they can be termed “Pink Elephants.”
The Foley scandal, and the cover-up that accompany it, have also given rise to a new interpretation of the acronym GOP (generally held to be derived from Grand Old Party). This has now been waggishly rendered as "Gay Old Party." (cf. the expression "gay old time.")
The reinterpretation of the acronymn reflects a practice that has been going on for some years, as when conservatives spoke of CNN (perhaps unfairly) as the Clinton News Network.