If you have a volt meter, now is the time to use it. When making voltage measurements for the Purple wire, use the same ground location for the DMM as you used for the AVCC. When seeking grounds for any aftermarket goody, the battery is best ground #1 (as well as any terminal strip that is directly grounded to the battery), the engine is poorer ground #2, the main frame is even worse ground #3 and the rear sub-frame is the worst ground #4.
Is there *anything* on the brake circuit that is not 100% OEM? Sometimes even when there are no LEDs, Back-Off flashers, etc., there is still a small bit of voltage left on the brake wire. If this is the case you may have no choice but to use a brake actuated relay for the Purple wire.
If you relocate the Purple wire and it still doesn't work make sure that your brake peddle & brake switch are mechanically working correctly.
It will be worth all this effort!