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.
I was told by my parts guy that the back up light switch is the same as the reverse light switch.
You pull back on the turn signal switch. I believe the Classic that year might have still had the floor-mounted high beam switch, though.
The neutral/back up light switch is located on the passenger side of the transmission close to the rear corner of the housing. It is triangular in shape. Take it apart carefully and clean the contacts with contact cleaner.
It is a three wire switch on the driver side of the transmission.
On my 96 Cherokee Country there is a button on the underside of the switch that releases the knob and shaft and the shaft just pushes back in until it catches.
the back up light switch is located in the gear shifter console
On my 1993, 1 is Brown/with a light green tracer, the other is black. If the bulbs are good & the sockets look O.K. The Back up lights then go to the transmission. Right side reverse switch or some say neutral safety switch.
switch is on the transmission
You can try to reset your brake light switch by unplugging the brake light switch and plugging it back in. If that does not solve your problem you will need to replace the brake light switch.
the back?
The jack should be either under the back passenger seat or behind the spare wheel if mounted to the wall in the back.
check the plug at the back of switch it may be loose