Thanks for the responses.
DaveN - The assembly is held in place by a couple of holders (not sure what else to call them...) which I'm guessing serve as the electrical connectors as well, as I don't see any other connectors. When I place a voltmeter across the connectors after removing the brake light assembly, and press the brake using a long stick, the regular brake lights come on, but there's no voltage between these two connectors.
As far as the assembly itself, its behavior is kind of flaky. When I take it apart and connect it to the car battery, five of the seven bulbs light up. I just happen to have several spare bulbs, so I installed them in place of the two that weren't working, and only one of them lit up. I wiggled the one int he bad position, but it didn't help. I then swapped one of the older, working bulbs, with the one that wouldn't light up, and even with the new bulb, the bad position still didn't light up. Then I wiggled the bulb in its connector some more, and was finally able to get it to light. So my guess is none of the bulbs were bad in the first place; I just have some flaky (or "dodgey" as the Brits like to say) connectors. However, even after I was able to get them all to light, the assembly still won;t light up when I pout everything back. So it seems, as is so often the case with me, that I have multiple problems <img src="/forum/images/smilies/968/sad.gif" class="smilie" alt="" /> .
I've heard several people say replacing the bulbs with LEDs is a good idea. Are these a straight drop-in, or do I need a whole new assembly? What type/size LEDs would I need (I don't know much about LEDs)? Do I need to wire a resistor in series with them? Basically, could someone please provide a step-by-step procedure as to how to convert to LEDs? However, bear in mind that I'm selling the car, so I don't want to get into any expensive upgrades at this time. My goal is to get the assembly back into proper working condition, not to improve upon it, unless as improvement will help solve the problem. But I think the root cause of my problem is that I'm not getting any voltage to the assembly. Or, as DaveN says, maybe there's a problem with a related system. Last time I checked, the door LEDs were flashing when I lock the car, indicating the alarm is working. In fact, I've set it off a few time recently during various electrical troubleshooting exercises.
Thanks again.