Here's a clip of Neil Sedaka acting in the 1968 film The Playgirl Killers. What I found surprising about this clip is that someone at the Little Green Footballs blog has linked to it!
Neil Sedaka, if you look carefully, changes into six different outfits in this Scopitone video of "Calendar Girl"! Good thing this was obviously filmed in multiple takes, or he would have given Gypsy Rose Lee a run for her money. :)