I want to install aux. backup lights and not wiring them to the jeeps backup ligts. I don't understand the switch. It has three prongs on the back The diagram shows one is power coming from the relay one is for the ground and the other is for attaching to the headlights (these are fog lights) so do I not use the prong to the headlight? And are 55W fog lights ok to use. and do they need to be a certain height and width?

sold my 88's (had 2, one yours, and one Comanche)
sold in 2000 year, ran hard and over 250k miles each.
the answer is the same,as all cars, for sure..
you have an added relay for lights.(aux)
this relay prevents overloading the cars H/L wiring and fusing
so there are 2 parts, there, a relay and a fuse inline added.
the fuses are are for fire safety. (the battery can do 500+ amps ok?)
Relay mounted somewhere, and...
the coil pin 1, ground. car body ground is ok.
then the relay coil 2 wire to the H/L low beam wire,or tail light wire using and inline 5amp fuse , to protect that very expensive H?L switch in that jeep,
tail lamp wire also means PARKING lamps. TODAY.

Contactors are those switch part of relay not the coil.
then contactor, power in pin to one more fuse, 15amp to battery +
and each contactor out to your plow lights. (load)

the when H/L are on the relay closes and the Plow lights work
if you google this there are zillions of wiring diagrams for this
even 4wd offroad light bars wired the same way.

there you go, how to wire AUX lights on any vehicle.

use a fuse never un wires unfused, ever
it works just like a flash light.
battery > switch>>> lamp.
so if the lamp is stuck on the switch is shorted.

"...reverse, but the light stays on, all the time."

Sure it was the switch? there are three things that go bad on the heaters. First thing is the blower resistor. the second is the blower motor and third is the switch. The go bad in that order most of the times. I replace a lot of resistors, some blowers and rarely the control panel/switch.

Your old one had one wire connector and one prong, the new one you put in has two prongs on the switch and the connector so what did you do with the extra wire on the new plug? You put the new two prong switch with the old one wire connector.

this may be an update or wrong part, why dont you go to an autoparts store and get the switch, tell them you have a gauge.
let me check this out , just give me a minute ...............

Okay, i checked this out and there are two different switches
the two prong is for the gauge and the one prong is for the light.

I know you have a gauge, return the switch and sensor they are wrong that system only has one wire, the problem is that this jeep a 1996 has a 1995 engine in it, that happens all the time when they are making any type of car or truck, go to the auto parts store and tell them you have a 1995 jeep grand cherokee with a 4.0 engine and you need an oil pressure switch and you have a gauge, they should hand you a single prong switch. put it in and let me know what happens. good day.

The neutral switch is so that you can't start your vehicle in a gear (drive, reverse, ect.) your looking to replace the backup lamp switch. Not sure where its located on your jeep but that sounds like the problem. Happy hunting!

the backup light gets its power from the neutral safety switch on transmission.
\When you put vehicle in reverse it toggles the switch in the tranny to engage the backup lights.
if that plug has the wire broke off the backup lights will not work.

Tail light and backuo light are separate circuits. Backup light is under the control of the backup switch located on the shift lever or transmission. Thats why one might work right and not other. Most troubles of this type are due to poor ground connections Check again what you did to change the tail light assembly

could be the brake switch went out of it

You are correct, Power flash and ground.

on the transmission