Does the rear plate on a 1967 just bolt up to the holes in the body or is there some kind of bracket?

No bracket - just two(2) small plastic inserts that have a square back to go through the holes in panel and then the license screws expand them to keep in place.
The plastic inserts are available at most auto parts stores in the Dorman/Motormite "HELP" assortments.

no bracket on 67-68. white square nut things (2) that pop into the square holes. Only one rubber bumper to keep the plate off the paint, and screw it on.

no bracket on 67-68. white square nut things (2) that pop into the square holes. Only one rubber bumper to keep the plate off the paint, and screw it on.

Actually, on my '67 there are two rubber bumbers to keep the plate off the paint.

Thanks!