So I was just rewatching the vid again when I noticed the song in the background gets caught by content ID nowadays, So I searched up the song here:
And turns out the top comment is from a Tom D'Antoni who talks about using the song to make car commercials in the 80s, and when someone asks him if he made Big Bill Hell's, he replies yes.
If you check out his channel he has some reels of his actual commercials that he uploaded in 09, and on a comment he replies with a blog post about the process of making the commercials here which at the end of the blog has an explanation of how Big Bill Hell's came to be.
Looking around online I didn't see him credited anywhere else, so I'd thought I'd throw it out there.