Try replacing the back-up light switch. It is located on the left side of the transmission. It is a common problem.
You will need to check the ground wires. A loose ground wire can cause the lights to work sometimes and sometimes not to work.
Check your fuses
head lights won't work, no power to them, signal works , reverse lights work
Try bypassing the reverse light switch that plugs into the transmission. If your reverse lights come on, voila! Problem solved. Buy a new switch.
The problem is the reverse light switch. It is located on the top of the transmission that should sloved your problem.
the reverse light switch is either out of adjustment. or broken. new one should be fairly cheap
Replace the bulb first, if this does not work try the reverse switch.
98 sierra1500 4x4 all lights work excepttail lights fuses are good bulbs are new
check nutral safety switch
what to do if my reverse lights on my 1993 gmc 1500 truck wont work
check your back up light switch
there is no fuse for the reverse lights check the netural safety switch it may be out of adjustment or shorted.