Usually a sign of a bad ground or a problem in the light socket.
Dont do it... It will take you bout 30 minutes to remove and replace it on the steering column
I would suggest that you take a look here (I used this to correct brake-light issues on my '01):
Many Grand Cherokees have had this type of issue. The thread is lengthy, but does cover just about every type of issue known with the tail/brake lights.
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.
First, I want to say thank you for the info, you saved me money and aggravation. Second it took mea little while to figure out what contact I was looking for. So I would like to provide a little more detail to make it easier for others in the future.
This is the corrective method for your brake lights not working when your headlights are on(2000 Jeep Cherokee Larado).
1) The cause of the problem is heat from the bulb.
2) Remove the light assembly as if you were going to change a bulb.
3) Turn the socket and remove it from the taillight assembly and set it aside(check to be sure your bulb is not burnt out).
4) Look at the opening, you will see 3 flat chrome colored contacts on the assembly.
5) Notice the one by it self at the top of the opening, that is the "ground".
6) If you look closely you will notice the plastic around the ground contact has shrunk a little bit, this caused the contact to pull away from the socket, causing the problem.
7) With a small flat head screwdriver, VERY GENTLY pry up the contact so it stays slightly upward by itself.
8) Re-insert the bulb assembly back into the housing and press your brake petal with your lights on.
9) You should be in good to go!
10) Tools: Phillips head screwdriver and a small flat head screwdriver.
11) Time : 5 minutes per light
The tail lights and the brake/turn lights use the same bulb but, there is 2 filamants in the bulb. One for tail lights and one for brake/turn lights. So just because the brake lights and turn signals work doesn't mean the bulbs are good. If bulbs are good you can check to see if there is power getting to the tail light assy's by unplugging the connector at the assy and using a test light probe the connector (harness side) with the headlights on. If you are getting power to the assy the test light will light. To make sure, turn off the headlights and test light will go off. Hope this is helpful. Good luck.