[VetteVet]

Look for a fuse in the panel labeled B/U lights. It's a 10 amp fuse. There will be a dark green wire going from the fuse panel to the steering column to the neutral safety switch. Another green wire runs from there to the firewall connector by the accelerator linkage behind the distributor. This wire then runs under the cab and along the frame to another connector along with the rear tail lights and the brake/turn wires to the rear lights.
If you have a standard transmission then the wire from the fuse panel will go through the firewall block to the back up light switch on the transmission and back to the cab connector behind the distributor. Check for power at the fuse then jump the green wires on the NS switch or the trans switch. If the lights work then the switches or bad or out of adjustment. If not then the wiring or the connectors or the light socket grounds are no good.