I just discovered this evening that my rear lights do not work. My brake lights work when I activate the brakes but when my foot comes off the brake pedal all the back lights are off. I've checked all the fuses. I've checked some relays you can't seem to find any reason why the lights won't function
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Have you checked that the fuse that supplies power for the taillights etc is tight in the fuse holder in the fuse block?
If all the lamps aren't working you need to start checking the 12V from the fuse block fuse¹ to the taillights etc and check how far you get before it's not there. The earth to the tail lamps must be OK because you said that the brake lights work and they connect to the same earth (for each taillight)
Here's an image from the 2002 Buick Century service manual showing the wiring for all the lamps that will help.
Since no lights are working it may be a faulty wire or connection between the fuse and the multiple connection point S408 as this is where it splits to go to the left & right sides and the license plates lights etc
¹ In the 2002 model it is fuse #17 in the instrument panel fuse block
(click on image)
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