The problem is the reverse light switch. It is located on the top of the transmission that should sloved your problem.
They are called mini blade fuses Fat Pete
Check your fuses
Try Replacing turn signal flasher
have you checked the bulbs and fuses
check for blown fuses
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 reverse light switch is either out of adjustment. or broken. new one should be fairly cheap
I have 2000 accent, my fuse box is to the left of your feet as you sit in the drivers seat, on the side panel. There should be a small door. Hope this helps you out.
check bulbs, fuses & reverse switch
Check the diodes in the fuse box under hood and in the box in interior on the driver's side. The are black and look like mini fuses. Littelfuse makes them and they are also available from dealers. It's common they lose their resistance.
I'd check all the fuses
The 2002 Cavalier has a reverse light switch. The switch can be bad, or have a loose connection causing the lights not to work.