Be sure to check both fuse boxes one on the passenger side kick panel and under the hood.
have you checked the bulbs and fuses
have the reverse safety switch checked if this is not working it will stop reverse being engaged this is done so as not to engage reverse by mistake
Have you had your u-joints checked?
have your motor mounts checked one is broken
get the universal joints checked on your driveshaft.
have the u-joints checked on the driveshaft.
the reverse switch in the transmission
There's probably something wrong with the reverse gear. Have it checked by a mechanic then see how much it would cost to repair it.
have your transmission checked, you need a new one.
It depends on your personal preferences and needs. If you often park in tight spaces or have difficulty seeing behind you while backing up, a reverse camera may be worth installing. It can provide an additional level of safety and convenience while driving. However, if you do not often experience issues with visibility while reversing, it may not be necessary to invest in a reverse camera.
In the 1988 Nissan the alternator, instrument panel, and backup lights shared a fuse. Before changing a fuse see if the backup lights work (have someone watch when you are in reverse). If the neutral start/backup light switch is broken internally, it can be blowing the fuse when you put the car in reverse.
Probably none