This is all new to me!
Is there an image of what the TWOK badge actually looks like without the Starfleet insignia on top?
Yep. When It's a Wrap!
was auctioning insignias, there were a few that had fallen apart. And there is a still of someone's (in ST VI - Kirk's?), where it has been reassembled upside down in a few sequences (the dot is on the lower left, not upper right.
The one that David Marcus wears in ST III was revealed in It's a Wrap!
pics as a different-but-similar citizen's version without the Starfleet insignia.
Was this ever documented anywhere? like a fanzine tech manual? I don't remember this detail...
It took a while for definitive info on all the rank insignias for ST II-VI to filter out, too. I recall ordering a set of resin insignias from Intergalactic Trading Post or Star Tech in January 1984 and the card they came fastened to was labelled. Until then, it was all guesswork, from ranks identifed onscreen by dialog.
The trapezoidal "chief" epaulette badges worn by Rand in TMP were wrongly identified by several mail order catalogs as being for the back of the flaps in the ST II uniforms, as were some round UFP badges - but, of course, it is possible they were
both used as "security doodads" if there were so many variations in use.