Check the backup light switch.
The 2002 Cavalier has a reverse light switch. The switch can be bad, or have a loose connection causing the lights not to work.
Try checking the neutral safety switch. This switch is the one in automatic transmissions that makes the backup lights "flip" on when going from park to drive as you go through the gears. When my neutral safety switch shorted my backup lights stayed on constantly.
Check Fuses, Replace Bulbs, Replace Shift Position Sensor. End of solution
It could be caused by a bad ground or severed wire somewhere.
check your bulbs and fuses check your bulbs and fuses
Defective reverse light switch.
Check the fuses Check the backup switch Check the wiring - make sure that there is good contact.
Start with checking the fuses and bulbs. See sources and related links below for bulb information.
have you checked the bulbs and fuses
The lights on the trunk are only back-up lights and nothing else.
that points to a broken wire to the light, a bd ground wire or a bad light switch
on some cars the tail lights and brake lights are totally different bulbs gain access to the bulbs and have someone push the brakes so that you can determine which bulbs are the brake lights and replace the tail lights