Brake lights must go through the T/S switch. It is the job of the switch to cancel out the brake lights when turning. Since you have functioning lights independently of each other it would seem that the problem is in the switch or the wiring.
What wires from what I have go from the box to the brake light switch. What wires are connected to the brake light switch and where do they go from there. My only issue is having the turn signals cancel out the brake switch when applied.