Well, I wasn't thinking of it, but thanks to your suggestion, I found it on YT. I cut back and forth from a comp dvd from the late 80s, in which it was used, and the YT video. You've convinced me that what I have on my dvd is James Darren, slowed down to a good FT tempo. It sounds AMAZINGLY like Sinatra. I am not often fooled by Sinatra wannabes, but this time, I was.
I can now stop dreaming of finding the song. Alas. Amazing that Sinatra never recorded it; it's Van Heusen/Cahn, and even, I believe, a Riddle arrangement.