This is the b-side of "Sometimes Good Guys Don't Wear White." My best guess from the Tower label catalog number is that it is from about mid-1966, maybe summer, although it certainly could have been recorded earlier. (The 45 is catalog number 257 and the entries on Discogs for Tower single releases from 1966 stretch from records numbered 195 to 298.)
Producer Ed Cobb wrote "Sometimes Good Guys Don't Wear White," but this b-side was written by drummer Dick Dodd and guitarist Tony Valentino. It's one of two songs written by them that appear on their first Tower LP.
I would say that this is a pretty exploratory song for mid-1966. One verse and then, seemingly, a chorus. Then, at 1:15 what appears already to be a bridge. Not a bridge that just goes eight measures and is done, but one that modulates to a different key and takes an unusual, fourteen-bar journey back.
After this, the song becomes unusual in how abbreviated it is rather than how exploratory, never even constructing a second verse but just riding out the chords in a long vamp for a quick ending.
So, to the extent that someone might consider unusual song structures as one of the most compelling things about how rock music was evolving during the time (in some cases, at least), this record feels like something that was on the cusp. It also seems to me to be state of the art in a number of other aspects, a guitar intro possibly influenced by the Who, power, subtlety, creativity, and repetition in the rhythm, and that power tempered by the prettiness of their chords and their vocal harmonies.