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It could've been a cover the band did of a song by a different band, and/or a song that only showed up on a concert tape or bootleg. I realize that's not the most helpful, but have you tried hitting up music forums/communities? That sort of thing did used to be pretty common, and the mixtape crowd of yore might be able to help you.

This was a song that some people I occasionally hung out with in the early/mid 1980s would play on their boom boxes. They said it was by Violent Femmes; I very specifically recall that I was told that the band used a Mariachi bass (aka guitarrón mexicano). The thing is, I've just finished listening to every song that Wikipedia lists as being on their first two albums - plus the singles "Ugly" and "Gimmie the Car" - and none of them struck a chord with me, so to speak. The only thing I really remember is that the song has an Epic Riff, though I don't remember what the Riff sounded like, merely that it had one. The song "Blister in the Sun," their only song listed on this wiki as having an Epic Riff, doesn't sound familiar to me. I went off to school in 1985 and stopped hanging around with them, so it must have been released before that year.
Three options I see:
UPDATE 01/18/2024 I just found it by accident. "Add it up." IDK why I didn't know it was that one when I looked into it in 2016. Anyway, closing. (That's new since the last time I logged on.)
Edited by randomsurfer