To eliminate circuit backfeeding you will need to establish perfect ground connections to the rear lamps. But, there is a problem with your wiring logic, too.
Light green is backup (reverse), dark green is right turn/brake, yellow is left turn/brake, brown is tail/park/license plate, black is ground. Unless the third brake lamp contains a logic circuit, it will need to draw power from a dedicated brake lamp wire that connects directly to the brake switch, bypassing the factory turn signal switch and rear lamp wiring. Otherwise, it will flash with the corresponding turn lamp.