Brake lights

Using a voltmeter or at least a twelve volt test light check for voltage going into and out of the brake light switch with the brake pedal pressed down a few inches at least.

Sorry about that, I see this actually has a brake pedal position sensor.

I do not see a test for that only a calibrating procedure.
I suggest you first scan for any codes relating to that sensor or the brakes and try the calibrating procedure if no codes found.
Calibration procedure:

1. Apply the parking brake.
2. Place the transmission in the "park" position.
3. Install a scan tool.
4. Clear all BCM DTC's before proceeding.
5. Navigate to the vehicle control systems menu.
6. Select module setup menu item.
7. Select BCM menu item.
8. Select the BPP sensor calibration procedure and follow the directions displayed on the screen.

If anything first try a new stop lamp fuse number 47 or test both sides of it.