Most common problem is poor earths and or bad contacts within the fuse box/fuses.
First thing would be to try rolling over the fuses in the box with your fingers. If the fuses are old, they may have oxidized? on the ends. Either replace or give them a light sand. Same goes for the fuse holders themselves, clean them up and make sure the pins have enough tension on the fuses.
Re reading your post, appears it is the just the rear lights?
Yes they earth thought the body. Again, clean this up including the clips on the bulb holders. Seperate earths cant hurt.
Shaun