All sorts of strange things can start happening if the earth connection to one or both lamp clusters fails, or has a high resistance.
Things like indicators stopping, or the flash rate changing when you apply the brakes, the front sidelights lighting up instead of the brake lights, all the lamps in one cluster glowing dimly when only the brake lights are supposed to be on, or the tail lights going out instead of the brake lights coming on, etc. etc. can all point towards a dodgy earth connection somewhere.
Just to complicate things, the fault often isn't at the light cluster where the lights come on unexpectedly, it is just as likely to be on the opposite cluster.
The fault can back feed 12 Volts through all the lights in the faulty cluster. That power then flows 'backwards' through all the circuits until it finds an earth connection, lighting all the other lamps on the way).