It is worth checking all the earth connections, including ones in the dash, as any bad earths would allow current to flow back through other parts of the circuit and eventually find their way to the lamps. The earths needn't even be obviously to do with the rear lights. Given you are using LEDs then there should be diodes in the units to ensure the correct polarity, however, your dashboard repeaters would still be filament lamps and so could still allow current to flow back down the circuits to the tail lamps.
If you have any current flow in the system then you could use this as a tracking system to figure out the current flows. Usually there would be current still flowing to clocks, alternator, alarm, etc so you can pull the connections on these in turn to isolate the suspect area of the vehicle.