Hi Neal. If it is the same as my 32 2 door sedan the screw hole is for a 12-24 screw that goes into a captive nut in the bottom of the rear window channel. The top of the channel has a single screw (self tapper) into the door frame.
I might have showed it in a video.
Check this:
https://youtu.be/O8diW3_fuko?t=109
Not sure about the "rivets", unless they are the remnants of rusted self tappers from holding the door cards on.
Mart.