You may have seen “Psycho Beach Party,” director Robert Lee King and writer Charles Busch’s wickedly funny send-up of classic Hollywood, while surfing on late-night cable channels in the early aughts.

Before Jaws made us afraid of the water, Hollywood made it the hottest place on Earth — filled with tans, tunes, and teenagers who never stopped dancing. From the late ’50s to the late ’60s, ...