Leaving work today my backup lights decided to turn on for the first time since I've owned the truck and not shut off the entire drive home. I unplugged all the wires from the transmission, pulled the fuse for the backup lights and they still remained on, so I just pulled the bulbs out. After a quick interwebs search it looks as if the neutral safety switch is bad, so I got one coming for tomorrow at the parts store. I could see if the switch was bad the lights not coming on in reverse, which I assume was the reason they never worked before. But what would cause them to come on all of a sudden and not go out even after pulling the fuse?

Short to power?

As far as I know even my truck requires the key to be ON to get backup lights to come on.

 Correct me if I'm wrong, but the neutral safety switch would control the power to the backup lights? So by unplugging the pigtail should have caused a break in the wire? If not then pulling the fuse would cause a break in the power supply... I'm not an electronics person so I'm clueless here.

 Key on or off, unplugging and re-plugging in the neutral safety switch, and moving the shifter through all the gears didn't have an effect on turning the lights off.

 Is there anything else the backup lights are tied into?

Here is the wiring for it...

 

backup.pdf

I would say a short to power somewhere after the neutral safety switch. Pull all the wire loom and tape off the trailer wiring and inspect all the wires closely especially if it's not factory. 

I'll have to pull it in the garage tomorrow after work and see if I can find any breaks in the wire.

I am gonna bet you have a short in the junction located above the drivers front wheel. 

 

that junction carries all the wiring for the bed of the truck

The trailer/tow option/connector takes a wire for reverse lights to the trailer for reverse lights on the trailer.    I am betting that the trailer constant hot is now touching the neutral safety wire on the rear end of the vehicle. 

Hope you find it!

GL

Hag

2001 FSM Ram 8W-54-3.pdf

I have also seen internal corrosion problems on the trailer tow plug under the rear bumper. If that thing gets corroded inside or on the plug going into the back of it, it can short things out too. Just another thing to check and keep in mind.