[DW SD]

I would guess that you may have single filament bulbs in the rear taillight housings where you should have double. The rear tail lights have two filaments, 1 for brakes, 1 for running light. When you hit the brakes the lights power up the other circuit. Just a guesss.

The single filament bulbs have their connector to positive in the middle, where the double filament bulbs have two contacts, but considerably offset from the center of the bulb. That center contact can connect both circuits.