Here are a few pictures I took of a good Tail Lamp Failure Module (wow, the name even kind of implies that it will cause failures)...
The "Jumper of DOOM" is the most common point of failure, then fractured solder unions for the harness socket, then oxidation of the harness connector and socket. Typically, I've found that a corroded harness and fractures in the solder only cause intermittent failures or lights that are just dim but with a persistent dash indicator. The jumper I've seen completely burn holes through the board and cause a complete lighting failure.
"R1" and "R2" are used to calibrate the sensor for a certain load. If you convert to LED lighting you may be able to keep the failure sensor in place by swapping these out with a different resistor (use a potentiometer to find the value, test it with a meter when you find it and then swap in a resistor for that value).