I just solved the same problem. In my case, the replacement switch was poorly designed.
There are three wires going to the backup light/neutral safety switch. You can use a test light or volt meter to confirm you have voltage being supplied from the fuse to the switch by measuring the voltage at the connection corresponding to the white wire (ignition ON). While the connector is disconnected, you can check the rest of the system (assuming the white wire is hot)by jumping the outside connections on the connector (NOT THE CENTER!) with 12 ga. wire while an assitant (or a mirror) tells you your backup lights are on (be careful not to short the wire to ground, it will at least blow the fuse, cause sparks and other nastiness). If so, the switch is the culprit, If not, your troubles are in the wiring between the connector and the lights in the trunk.
If you pull the switch out, you'll see that the switch has a metallic pin in the very center (inside the transmission), that must be all the way OUT for the backup lights to work. Remove the switch with a 1" box wrench (you can get there from underneath, without jacking up the car even), plug the connector back on, and with the ignition ON, push the pin in and out. When the pin is out the backup lights should light up. If not, and jumping (see above) the connector worked, your switch is "no good".
If the lights light up with the pin out, but it doesn't work when installed on the transmission, it could be, as mine was, that the new switch is TOO LONG, and doesn't ever allow the center pin to come all the way out and light up the lights. I used a for-real Chrysler switch from the junkyard, and now all is well. Wish me luck returning the switch I bought.
If you are curious, you can see how it work internally by placing a mirror strategically and shining a flashlight off the mirror into the hole where the switch goes. You'll see a spot, when the tranny is in reverse, where the plastic has a dip in it to allow the pin to come all the way out. If the switch is too long, the pin never goes all the way out despite the dip, and the lights remain dark. You can also see how the neutral safety works too!
Here's an alternate solution if the switch is too long. Put a shim of some kind on the switch like, a washer, to push the switch out farther.
Check the backup light switch.
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.
If the bulbs are the cause, remove the tail light assemblies and replace the bulbs; if they still don't work, replace the neutral safety switch, located on the front of the transmission.
Check bulbs and switch
check fuse and bulbs...switch
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.
well it seems to be a common problem it might just be the switch on the transmission
Check bulbs Check fuse Check switch
Check bulbs and switch
Fuse, bulbs, switch, wiring.
Bad bulbs, bad switch located either on steering column or on transmission
There is no adjustment for the backup light switch. The switch must be broken or the fuse is blown or the bulbs are blown or the wiring is damaged.
Bulbs? Open wire from switch to lights? Corroded light sockets? Bad ground?
Both bulbs are out, wiring problem, switch problem, fuse, relay.
faulty brake light switch (on pedal)
Check the fuse, check the bulbs, check the brake light switch, in that order.
There is a switch in the transmission (manual) and I believe also automatic that triggers your backup lights when you move (change gears) into reverse. If the switch (in the transmission) does not touch (trigger) the backup light switch; or if the switch is not working; you will not have any reverse lights. Also , if you have had any changes in your transmission due to lifting the body, or changing the original transmission; the lever that triggers the switch may not be able to come in contact with the backup light switch in the transmission. If you have this switch replaced by a garage it may run around $160 for the switch and another $100 to $200 for labor. If the transmission does not trigger the backup light switch in the first place ,due to changes in the transmission, or a body lift; then changing the switch will not make any difference; the backup lights still will not work.
Check bulbs Check fuse Check the operation and adjustment of the stop light switch
Bad parking/tailight fuse? Open in rheostat (dimmer switch)? Bad light switch? Bulbs?
Could be a couple of problems, one lose wire in pig tail harness, but since you say its both back up lights it may be a relay switch when you place into reverse the switch does not respond to activate the lights
First check the bulbs, then check the fuse, then check the switch on the transmission, and last check the wiring.
Possibly blown fuse, bad brake light switch, or blown brake light bulbs.
Blown fuse, failed switch, broken wire, burnt out bulbs,
Check all the fuses. If not bulbs or switch that's all that it can be,
check the ground for the lights