I would like to thank firstname.lastname@example.org for his January 1, 2005 post at http://www.carsurvey.org/reviews/jeep/grand_cherokee/r33943/comments/page-2/
His instructions successfully fixed my problem i.e. my lower rear brake lights don't work when I have my headlights switched on.
The problem was correctly predicted as a faulty ground contact on my brake light, and I cleaned the contacts (I cleaned the other two while I was at it) with a Q-tip dipped in rubbing alcohol, and raised the metal contact slightly (be very gentle) on the ground contact with a small flat head screw driver, that I had to tighten up the screws in my reading glasses.
The whole process took me about 10 minutes for the first brake light, and 5 minutes for the second light (since I knew what I was doing second time around). My local Jeep dealer quoted me $376 to fix this problem by completely replacing my two rear light fixtures (2 x $168 for the fixtures and $40 labor costs) and I fixed it myself with the help of this web site for free in 15 minutes !!! I am an office worker, not a mechanic, and not particularly mechanically minded, so if I can do it, anyone can do it.
Here is a very useful site, which shows you how to remove your rear light fixture so you can fix this problem http://www.wjjeeps.com/lamps/lampsrem.htm#EXTERIORREM
And if the trick above doesn't work, here is a site where you can order replacement light fixtures for $58.95 each instead of $68 each list price, which is what my dealer quoted to me. By the pay the part numbers for the replacement fittings are 11-5275-01 (RH passenger side light) and 11-5276-01 (LH drivers side light). The web page is at
Tools you will require for this job are (a) a Phillips head screw driver for removal of your two rear light fixtures, (b) a small/tiny flat head screwdriver for raising the metal ground contact, and (c) Q-tips and rubbing alcohol for cleaning all the contact points.