The brake lights on a 96 Jimmy are operated by the brake light switch, mounted on the brake pedal assembly. If the switch is bad the lights could stay on or off, or be sporadic.
Bring to a shop that has an ABS scanner to determine the problem
how to trouble shoot for gmc back up lights?
Check the brake light switch. It's probably attached to the brake pedal, under the dashboard.
The GMC dash tail and parking lights are on a different fuse from the brake lights. Check the fuses for a possible blown fuse.
Check bulbs they are double filamented smaller for brake lights larger for tailights Check fuses Check stop light switch
The whole turn signal arm unit needs to be replaced
There might be a separate fuse for the lower brake lights ( just a guess )
Did you replace the fuse? have you checked the circuit board well the lights go on cause they tend to short out often
Try changing the brake light switch located on the brake pedal shaft under the dash. There's a recall. google "multifunction switch recall jimmy" your dealer should fix it for free.
You need to be more specific about your problem, e.g. starter fails to work, lights do not work etc
In the compartment that holds the jack for this model, look for the wires near the rear it should be by the brake light but inside the vehicle. There should be a connection there for the light. If there is corrosion or a loose wire this would cause the problem of the passenger side working and not the drivers, I researched this dealing with no lights except the 3rd light working during braking, turns out it is the trailer harness connection.