2004 Cadillac SRX Rear brake lights on when not depressing

I wish it could be as simple as it used to be. On your SRX you have a brake pedal position sensor wired to you ABS module. The module sends power to the BASS relay to control it. Power goes from the relay to the turn/hazard flasher module, and that module feeds the lights. Any one of these could be at fault. When the lamps are stuck on, remove the BASS relay from the left rear fuse block(under the rear seat cushion, left side), the legend is under the cover. Do the lights go out? If there is an identical relay in that center, swap it and check operation. It could just be a relay. Is this something you are going to try and tackle yourself?

The clue with the brake pedal may be key in isolating a cause. It sounds like the relay is functioning properly, if you can get them to come and go by pedal position, you could have a faulty pedal position sensor, or wiring near it. With a scan tool, you could probably view that input. I can give you this much, it is a three wire sensor. Brown is the low reference or ground, yellow is the signal, and white is the 5 volt reference. A simple check would be to place a voltmeter across white and brown(harness side/disconnected), and check for 5 volts. It looks like the signal is varying resistance, this is probably to determine ABS strategy. I do know this, there is a BPP sensor calibration that needs to be performed if the sensor is replaced, and it requires a scan tool.

Here is a description of the brake lamps;
The brake pedal position sensor is a resistive device used to sense the action of the driver's application of the brake pedal. The brake pedal position sensor provides an analog signal that will increase as the brake pedal is pressed.

The brake pedal position sensor receives both a 5 volt reference voltage and a low reference signal from the electronic brake control module (EBCM). When the brake pedal is pressed, a variable signal is applied from the brake pedal position sensor to the EBCM through the brake sensor signal circuit. The fuse block left rear supplies battery positive voltage to the bass relay switch through the BASS fuse. One side of the bass relay coil is permanently grounded at G402. The EBCM supplies voltage to the bass relay coil upon receiving the signal from the brake pedal position sensor. The switch contacts of the bass relay close and battery positive voltage is applied through the bass relay switch to the center high mounted stop lamp (CHMSL), and to the turn signal/hazard flasher module through the stop lamp switch signal circuit. The ground for the CHMSL is applied from G402. The turn signal/hazard flasher module then supplies voltage to the left and right stop lamps in the tail lamp assemblies that have ground at G401 and G402. For export vehicles the stop lamps receive battery positive voltage directly from the bass relay.

And here is the calibration description;
Brake Pedal Position Sensor Calibration Description and Operation
Calibration Criteria
Brake pedal position sensor calibration must be preformed after the brake pedal position sensor or electronic brake control module (EBCM) have been serviced. The calibration procedure will set the brake pedal position sensor "home" value. This value is used by the EBCM to determine the action of the driver applying the brake system and to provide this information to the vehicle subsystems via the class II communication bus.

Calibration Procedure
"Â Install a scan tool.

"Â Turn ON the ignition, with the engine OFF.

"Â Select Chassis.

"Â Select DRP/ABS/TCS/VSES.

"Â Select Special Functions.

"Â Select the BPP Sensor Calibration and follow the directions displayed on the screen.