The brake light on my 2001 Jeep Grand Cherokee

see the diagram attached and proceed according for troubleshooting.

Usually, the brake light switch sits just behind the brake pedal. There should be a bracket with two-four bolts that hold it in. There will be a button the is depressed when the brakes are lightly pressed.
Please let me know if you need further assistance.
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2001 Jeep Grand Cherokee Brake Light Switch

i would check the fuses, and then all of the connection to the bulbs , to make sure that there is not corrosion, or shortage in the wires.

Very common issue is the lamp assembly (dealer item). They are very bad to ground back through the tail lamp filament, lights on the path has voltage on it and the lamp will not work.

sounds like a ground wire issue

there's a possibility that it might be the socket that the bulb actually goes into. my break light did something similar to that. the socket only cost about 8 bucks from the dealer.

replace the brake light switch, but first check the bulb and fuses

It could be the brake light switch located on the brake pedal

Id look at the headlight switch and do some voltage tests to see whats coming out of there. Pay close attention to any wires which look like someone was in there already.People can mess stuff up faster and better than the vehicle can by itself!

hmm interesting have you done any wiring to the lights at all?