Usually when this occurs it is because the brake light switch is either installed improperly, or the switch is not properly adjusted
Not being familiar with the Jeep Grand Cherokee, this answer will of necessity be generic in nature. There are two different brake light switch systems.
One is mechanical and the switch is inside the passenger compartment. In the other, the switch is hydraulically operated and is mounted on or near the brake master cylinder in the engine compartment.
Usually, the mechanical type brake light switch is mounted below the dashboard, just above the brake pedal. It screws into a threaded bracket. Adjustment of the switch is by screwing the switch farther into, or farther back out of the bracket.
The brake light switch is unusual in that it is a "plunger" type switch with a spring to hold the plunger extended, and thus IN THE ON position.
When the switch is screwed into the mounting bracket the proper distance it holds the switch in a position where the released brake pedal arm pushes the plunger in far enough to open the switch and turn the brake lights off. When the brake is applied, the arm moves away from the switch allowing the spring to push the plunger out, closing the switch and allowing electricity to flow to the brake light circuit and bulb filaments
If the brake light switch is "backed out" too far, then the brake pedal arm cannot push the plunger in far enough to open the switch and turn off the lights. Obviously however, it is close enough so that "lifting" the brake pedal [and its arm] can push the plunger in far enough to open the circuit and turn the brake light off.
IF your vehicle uses this type of switch, you can adjust it by screwing it into the bracket [toward the brake pedal arm]. Do this just a little [say 1/4 turn at a time], and check to see if the lights have gone out.
It makes the job a lot easier if you have a helper standing behind the vehicle to observe and report when the lights go out and on.
Once you have the lights out, then you need to properly apply the brakes to make sure you did not over correct, and that the lights do come on when the brake pedal is depressed.
Now, there is another type of brake light switching protocol that has a hydraulically operated switch that usually screws into the brake master cylinder [usually under the hood and on the firewall above the driver's feet].
IF it is this type of pressure operated switch, then I don't think there is any way to adjust it, and that means the switch is defective and must be replaced.
How to change the brake switch on a 2004 Jeep grand Cherokee Laredo
Yes.
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.
The brake light fuse on a 2003 Jeep Grand Cherokee can be found by looking at the cover to the main fuse box. It identifies each fuse and its location.
A short in the brake light circuit.
If equipped, it is above the liftgate glass.
They aren't. The brake light circuit is not connected with the headlight circuit.
You need to check the wiring for power to the bulbs.
passenger side fuse panel....#2
Mine simply needed brake fluid to fill it to the line indicated on the brake fliud container.
Defective or mal-adjusted stop light switch? Usually located at the upper end of the brake pedal under dash area
Check the bulbs in case they have fused, next check the fuse, and finally it could be the brake light switch which may need replacing