It is on the same circuit as the brake lights, but if they are not working, and the bulbs are good your switch needs cleaning or adjustment.
Attempt this first since the switch costs nearly $300 bucks.
On the passengers side of the trans just behind the bell housing there is a fan shaped switch, loosen the 12mm bolt ( smaller of the two, and rotate the switch while a friend checks the lights. this problem is usually accompanied by an occasional inability to start the vehicle, but can be cured by jiggling the shifter.
While adjusting the switch make sure that the vehicle will start in park as well, remember to block the wheels while testing the back up lights, engine off, key in run but not start, shifter in reverse, move switch until lights come on.
Once you find this spot, hold it in place and have your helper check to make sure it will start. This may take several tries to get both working correctly.
If you have no luck the switch may be dirty, this happens a lot. Hold the post to the bottom large bolt still while you loosen the nut, then remove it, then remove the 12mm adjusting bolt on top, remove the wire connector and pull the switch away, remove the bolts on the switch and separate the halves, use electrical contact cleaner and maybe some q-tips to clean all the copper connections completely apply di-electric grease and reassemble, refit to the trans and readjust so all functions work, this switch controls back up and start safety.
Caution! always hold that bottom bolt while tightening the large nut, this is connected to the gear adjuster and you could damage the internals if it isn't secured while you do it.
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 lights automatically come on as you put the car into reverse , if they are not coming on your most likely problem is the fuse or bulbs
Someone may have switched the sockets in the back of the lenses.
The backup lights on a 67 Camaro won't work if the bulbs have burned out of the shifter is misaligned. The lights come on automatically when put in reverse and will not function properly unless the shifter triggers the reverse sensor.
Very possible ... best to check the wiring with a voltmeter checking for +12vdc.
did you check the reverse switch on the trans ?
Fuse panel on the drivers kick panel, but your other lights would be out too. What you more likely have there is a reverse/neutral safety switch problem, when out of adjustment the lights will not come on.
True.
Sounds as if the wires at the rear of the vehicle are mixed up. Check to see if the brake lights come on when put into reverse gear. That will rather confirm the hosed wiring.
To let others know that you are breaking.
Take it out of reverse.
First check the bulbs and sockets with a 12v tester, if there is no current going to the bulbs then I would look to the back-up light switch as the problem. This should be on your transmission with a small wire harness coming from it. I hope this helps you. Mark