I think the turn signal switch is the culprit. Remember that the wires to the lights are power wires, and that the circuit is completed by grounding to the body. So I think the circuit logic for the brake lights goes like this: When the turn signal in not on the power is routed through the turn signal switch, bypassing the blinker device, to the brake light switch, and onto the brake light. The brake light stays lit continuously. When the turn signal is on the power is re-routed first through the turn signal switch, to the blinker device, and then to the brake light switch, and onto the brake light, causing it to blink instead of remaining lit continuously.