There is a short in the signal light circuit.
Try your fuses
Are you blowing fuses or are the bulbs blowing? Blowing fuses would be a sign of any wires or metal contacts in your brake circuit grounding out or shorting on themselves. You'll have to check all of the wiring in your brake light/switch circuit to be sure.
dash panel lights working? all fuses ok?, check on the fuses box under the hood it's a number 10 red, check if keeps blowing up
There are separate fuses for trailer signal lights in main fuse panel
If your fuses are good, the flasher is good, and the bulbs are good; There are two probable causes: Your signal switch is worn out, or you have a short to ground on the wires to the signal lights. Pick one or the other, or could be both.
Believe it or not, I have had to disconnect the cig lighter in order for the tail lights to work. Sounds far fetched but it does work!
Either hand signal or check and replace your fuses and turn signal bulbs.
Brake light switch runs through your headlight/turn signal seitch in steering column. This switch could be malfunctioning.
Check the wiring for damage or grounding problems and thoroughly examine the trailer plug if you have one. If you can't find any problems there, check the turn signal 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.
you probally have a bad wire that is shorting out and blowing your fuses.
you should try checking the fuses and replacing the bulbs the fuses for thos lights should only be about a 10 or a 15