Hotter After Dark (1967)

Nancy Starr hires Mike Malone, a local private detective, to get evidence of her husband's infidelity. Mike quickly takes the case and is soon hiding in the bedroom of Mr. Starr's mistress, Helen, and taking photos of Mr. Starr and Helen in bed together. For his next case, Mike is hired by a woman named Judy to be a bodyguard for Dr. Bernstein, a scientist who is in the process of inventing a device that will prolong human life up to 250 years. The deal is for Mike to move in with them, protect the doctor from foreign agents, and give stud-service to Judy. But though Mike checks the place for "hidden mics and strange devices," he's not only oblivious to Alice the maid really being a guy in drag, but actually starts making out with her/him.