Depending on the year, the MLPS or trans range sensor is out of adjustment. If you have driven like this for very long, you have probably done a good bit of damage to the trans already and should start saving around $1500 for a rebuild.
The backup light switch is mounted on the transmission casing.
True.
There is a backup switch in the gearbox. When you shift into reverse, the gear box switch contacts the switch and lights the white reverse lights. If you find that the reverse lights don't work it could be that the switch is not being triggered by the mechanism inside the gearbox. This is providing that everything else is working; wiring,bulbs,etc.
Either the switch that turns the backup lights on is out of adjustment, or has failed in the on position.
You have a short circuit between the backup light switch and ground. VWs are infamous for this because the power for the backup lights comes off the side of the ignition coil. When you stick the car in reverse, it grounds the coil and the engine dies.
check reverse light switch on transmission.
It's a matter of replacing the reverse position swith in the transmission. This switch tells the computer wheter it's in neutral, or reverse and when in reverse it triggers the reverse lights.
Where is the fuse located for the reverse lights
the switch needs adjustment
Both a stuck reverse switch and shorted wiring can be causes for reverse lights to stay on. Under normal circumstances, the reverse lights turn off as soon as the vehicle is shifted out of reverse.
Check your fuses
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.