Use a 7805 regulator with a clip on heat sink to get 12V down to 5V. Connect positive wire 1 to its input, its 'gnd' to your neutral, and its 'out' to a 1N4002 diode (forward biased) to the LED array. Connect positive wire 2 (from the brakes) to the output side of the diode.
This way, it always feeds 5V to the LED array, until the brake is actuated. Then the second positive line goes high, goes to +12V to feed the LED and the diode protects the regulator from seeing the 12V.
This requires a 7805 regulator in a TO-220 package, a 1N4002 diode, and a clip on heatsink for the 7805. Total cost, about one to two dollars.