These lights are all computer controlled ! Several modules involved DIM - dash integrated module , RIM - rear integrated module .They share information on serial data communication network . Class 2 an or GMLAN !
The rear fuse block supplies battery positive voltage through the REVERSE LAMP fuse to the coil and switch terminals of the reverse lamp relay. The DIM sends a power mode message to the RIM indicating that the ignition is in the ON position. When the driver of an automatic transmission equipped vehicle places the gear selector in the REVERSE position, the powertrain control module (PCM) sends a class 2 message to the RIM. The message indicates that the gear selector lever is in the REVERSE position. When the driver places a manual transmission equipped vehicle in reverse the reverse gear position switch mounted on the transmission closes. This provides a ground for the reverse gear position switch signal line, informing the RIM that the transmission is in reverse. For both automatic and manual transmission vehicles the RIM then grounds the control circuit of the reverse lamp relay . This energizes the reverse lamp relay, closing the switch side contacts and providing battery positive voltage to the backup lamp bulbs. The backup lamps are permanently grounded at G402. With both power and ground the backup lamp bulbs illuminate. Once the driver moves the shift lever out of the reverse position a message is send either by class 2 by the PCM or the reverse gear position switch opens causing the RIM to remove the ground from the reverse lamp relay control circuit. This opens the contacts in the relay turning OFF the backup lamps.
This is something best left to the dealer or a ASE certified repair shop . Need a factory or professional grade scan tool to diagnose an repair this . http://www.public.asu.edu/~pheanis/documents/VBI_CAN.pdf