The circuit grounds through the housing/body of car (no ground wires). If the lights just quit working without you doing anything with the housings first, and the bulbs are good, I would next look at the NSS as you have suggested. If you had been working on them before they went kaput, then recheck that the sockets have continuity to the housing and housing to the body. The NSS might not itself be bad - check its connectors and alignment before spending money on a new one.
Have someone move the gear selector slight forward and backwards while in reverse....and you measure out back....see what happens. Also see if you have power at the switch, or the firewall connector going to the reverse lamps. See your wiring schematic for colors.....black with red stripe???? Can't recall exactly... One pair of wires at the firewall are for neutral safety switch, and the other pair is for back up lamps.