The Turn Signal and Brake Light may be operating from the same Bulb, or separate bulbs. Regardless, the Brake light filament must be burned out. Another option is that the Brake Light Circuit is on a separate Fuse, and the Fuse is blown.
Check for those possibilities.
under the dash in the fuse box
because there is two filiments in the bulb one for brake and signal light and one for running light
replace taillight bulbs first. filiment from brake light can break and make a connection to your park light. pressing brake pedal can light up your turn indicators, or even park/dash lights
You probably have a turn signal bulb with two filaments one for the turn signal and one for the brake light. If the ground connection is bad on the turn signal circuit then the current would need to find another path to ground. The only other one available is through the brake light filament to the ground on the center brake light. Try removing the taillight assemblies from the vehicle look for what is probably a black wire screwed to the body or a circuit connection and either tighten the screws a bit or clean the connections.
If you have the same bulb for brake and signal, brake light power needs to be interrupted by the signal lights, The brake circuit has to go through the signal light switch so the problem could be there.
The brake light switch is behind the brake pedal.
I thought the same thing on the wifes car. I forgot about the third brake light, and was looking only at the tail lights.
You have to remove the trunk liner from the rear of the car,and then remove the three bolts that hold the taillight into place.
This is an easy one. Remove the two screws that hold the taillight to the body. They are located just inside the tailgate. The taillight has two tabs the fit into slots opposite the screws, so you'll need to swing the assembly as if you're opening it like a door. The brake light is the top bulb on the back of the taillight. This is assuming that you weren't referring to the "3rd eye" brake light, which I haven't done.
In many cases, the brake light and the turn signal use the same bulb.
Open the trunk and pull the carpet away from the corner by the taillight. You should see several black plastic nuts there, remove them but be careful to support the taillight assembly with your knee. The entire taillight assembly should now come away from the car and you can just untwist the light plug from the assembly. Pull the bulb straight out. Installation is just a reversal of the steps.
The 1993 Jeep grand Cherokee brake light switch simply plugs in and out. The brake light switch is located beneath the dashboard on the drivers side of the engine compartment.