I had recently replaced the rear bulbs, so went to Kragen (near Las Tunas and San Gabriel) and got a set of 4 bulbs (one for the top brake light, 2 for the lower two brake lights), on the unlikely chance they had burned out.
Will research if it is just a simple bulb replacement, or if a fuse has blown, or if the brake pedal switch has died.
All the rear brake light bulbs on the sides are not burned out. So the next thing to try is to replace what Jeep calls the "Stop lamp switch" and what anyone else would call the brake light switch.
It is located at the top of the brake pedal. Is creamy white colored, and really hard to get a picture of it! It took about ten tries, but finally got one to come out well.
So below is the picture of the "stop lamp switch" with the steering column on the left, and a zoom in detail of the part number stamped on it.
Went to my local Kragan, near corner of San Gabriel Blvd and Las Tunas, and ordered the Jeep Cherokee stop lamp switch.
Kragen part number S6075.
The part cost US$11, so very inexpensive.
They had the part in for me to picuup within two days (they rock!).
Online research on the procedure to replace:
The procedure for my 1998 Jeep Cherokee:
1. Using a 1/4inch drive 1/4inch socket, remove the bottom three screws to the kick panel below the steering wheel.
2. Now pull the plastic panel out towards the driver's seat. It is secured on the top with two spring pins, and the top should pop off.
3. Using the same 1/4inch socket, now remove the two upper screws of the inner steel kick panel. The bottom of the panel has two tabs that just need to pivot out.
4. Reach straight in, and gently rotate the switch counter-clockwise about 1/4 of a turn. The switch will just pop out! :)
5. Disconnect the electrical harness from the old switch by gently prying apart with a flat blade screwdriver.
Reinstall using the same steps, but in reverse order.