Were they not on one of the Pebbles/Nuggets albums as an earlier incarnation? I've got a feeling they were involved making "I can only give you everything" (the excellent riff being famously lifted by Beck)or some other garage classic.
I could be wrong, as I often am, but someone here is sure to know.
You're not wrong. Billy Gibbons former band was The Moving Sidewalks of "99th Floor" fame. Great garage single indeed. Their only album ("Flash") is a nice psych LP too.