Both back up lights dont work, where should I look to find the problem.
The backup lights are switched through the park/neutral safety switch mounted on the transmission. Locate the park/neutral safety switch on the side of the transmission where the linkage is attached. The problem might be caused from a poor connection at the switch. So try unplugging the switch connector and plug it back in to see if this gets the lights to operate. If not, it could be that the contacts for the backup lights are worn in the switch.
Tester