Village People songs, like cliches, are there for a reason.

Turns out YMCAs were tagged as a cruiser’s paradise long before the costumed boy band lampooned the health clubs’ rep in the 1978 hit single.

The dirty secret was out at least as early as October 1964, when Walter Jenkins, a 46-year-old married advisor to and longtime buddy of President Lyndon Johnson, got caught in a sting operation blowing an older dude in a stall in the men’s room of a Y just a couple minutes walk from the White House. (The actual club where Jenkins did his business has been rebuilt since he got stung.)

News of the sex bust didn’t break for several days — turns out Jenkins on the day of his bust went straight back to work at the White House after his release from the police station, and worked past midnight as usual.

But, when the story broke, just weeks before election day, it broke big. One biographer said Jenkins became overnight “the most famous homosexual in America.”

He resigned from the administration immediately.

Abe Fortas, a pal of Jenkins who talked him out of suicide after the arrest, reportedly told FBI investigators that, “It was common knowledge among Washington attorneys that the YMCA was the home of homos.”

There was no political second act around here for Jenkins, who died in Austin, Texas, in 1985.

Some history-revising conspiracy buffs have said that Jenkins was actually busted at the Hay-Adams, and that FBI head honcho J. Edgar Hoover changed the official scene of the tryst to the YMCA to protect the hotel.

If so, I say: Good for Hoover. There’s no way a tune called “Hay-Adams” would have played as well in the discos.