Defective reverse 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 replacing the headlight switch. Do the front parklights work and not the rear ones? If so check the harness to the rear of the vehicle for breakage.
you may have already checked, but to me it sounds like you have a loose connection at the battery
Very possible ... best to check the wiring with a voltmeter checking for +12vdc.
Check the brake switch at the pedal.
reverse light switch or wiring may be bad
the reverse switch in the transmission
Where is the fuse located for the reverse lights
Check your fuses
The light switch.
There are a couple of reasons why a 2005 Saturn Ion's reverse lights will not work. The fuses may be blown or the light bulbs need to be replaced. Fuses and bulbs can be purchased at any auto parts store.
Bad socket? Bad ground? Problem in steering column switch?