Yep, definitely a Shel Silverstein tune. Bobby Bare has recorded it twice---once on Drinkin' From The Bottle, and then from his latest, a 2020 release of a previously unreleased 1978 recording called "Great American Saturday Night"---which has exclusively Shel Silverstein tunes.

Here is the original Shel Silverstein recording from his Boy Named Sue album.
https://www.youtube.com/watch?v=UMmGb3tJbeA