while hooking up the brakes for this bike, I realized the bolt for the brake was missing. The brakes are gran-compe royals and I am wondering if anyone can tell me how these brakes work. As can be seen in the first photo, I tried threading the cable through this hole, then trying a couple lengths of 5mm bolt/washer to cinch the cable. However, there is not room for the sleeve to move and cinch the cable because it is already flush with the bolt/washer surface. I am wondering what parts I could be missing to make this work. Unfortunately the other (front) brake is of a different type, as in the last picture, so I cannot use it as a reference.

Cannibalizing parts off bike parts in the bike shop basement is where I would go..

looks like a short bolt screws into the cable, pinching it against the other piece with the hole in it.

From the top pic, all you need is a metric Allen bolt. Take the caliper to a hardware store and look at the M5 and M4 bolts.