The Fat Spy (1966)

It's a killer... a Diller... a blast of laffs!

A mostly-deserted island, which is believed to be the home to the fountain of youth, is off the coast of Florida. The island gets some visitors in the form of a teenage boy band, "the Wild Ones", and their gang of swimsuit-clad young people, who head there in a crowded powerboat ostensibly for a scavenger hunt.