The clip is from “The Garry Moore Show” which ran on television from 1958 to 1967. I couldn’t find the exact date for this particular episode but judging by the quartet line up I’d say it was probably 1959 or 1960. I was cellular at the time myself which I think qualifies as me “young people.” That must be why I like it.
The Gerry Mulligan Quartet was probably on the show to promote the 1959 album “What Is There To Say” but, interestingly enough, they didn’t play a song from the album. Credible sounding YouTube people seem to think the song they played was “Bernie’s Tune” with the melody removed. I tried humming the melody on top of the song they were playing and it fits perfectly so I’ll buy that and report it as fact.
The person who posted this video added absolutely no helpful information in the blurb so all hail “random YouTube commenter whose screen name had the word ‘jazz’ in it” for (probably) knowing the name of the song.” Also hail my buddy “Encyclopedia Brown” for knowing the song was introduced by Garry Moore. I seriously doubt my poor Google skills would have turned up the name so I’d probably have spent the entire post calling the poor man “Smokey The Host.”