Per the 1965 and 1966 Body Assembly Manuals, the 65 rivet was 380098-S, 7 required, which translates to a 3/16 nominal dia "Pop rivet", 0.450 body L, 0.375 dia head, 0.188-0.250 grip range and had a steel mandrel. The 66 versions used 380334-S, 5 required, all dimensions the same as 380098-S but it used an aluminum mandrel. The rivet used in the two upper corners was 380335-S that had a longer grip range, 0.251-0.375, but was the same as 380334-S.
I assume that there were customer complaints about getting snagged on the screws holding the fixed panels to the trap door frame so Ford went to a rivet. The same snag scenario probably applied to the five screws for the trim panel above the door so the screw protectors (375690-S and 380865-S) were used. The change from steel to aluminum mandrels is probably because the aluminum mandrels were easier to install, or a different vendor. The longer rivet was used to accommodate two panels to the frame at the corners. My 65 San Jose Fastback uses rivets, all the 66 Fastbacks I've worked on use rivets. I found both correct size Pop rivets, including the aluminum mandrel, for 66 use in a local hardware store, Orchard Supply, but that was years ago (their selection has deteriorated). I have some odd size steel mandrel Pop rivets in a 2 pound coffee can but haven't got around to sorting them. The sizes that Ford used seem to be industry standards.
Jim