Could be the reverse switch on the transmission, the bulbs, the sockets or the fuse for the back up lights. Test for power at the sockets if power is there then it the bulbs. if no power the check the fuse. If the fuse is good check the switch on the side of the trans for power in then power out when the key is in the run position and the trans in reverse.
Hope I helped
GM Tech for 20 years
