I think the LCM is in the $400 region and it has to be programmed on install, so keep checking other things first. What about your license plate light and the front parking lights, are they on? The tail light bulb is a 3157K that incorporates tail light and brake light and turning light, (I think mine has two of them per side, one above the other).
If the front parking lights are working then the problem is not in your LCM. So the bulbs are the most likely problem, although it could be wiring or connections, let's go with bulbs. The owner's manual refers tail lamp replacement to the dealer. I am sure access is from the trunk, so I will see what I can find.
Oh, that doesn't sound good. So next step is to check the connections at the LCM for that circuit. Are you having any other lighting problems? I will get the LCM removal procedure and charts for checking pinouts and wiring colours.
Attached is the test procedure for your main light switch. The terminal numbers are shown for each light switch position (Off position is a open circuit between 7 and 3; Park light position is a closed circuit between 7 and 3; Headlamp position is a closed circuit between 7 and 3).
1999 Lincoln Town Car light switch tests 149-1 & 2.pdf