Cadillac SRX 2011 car is off but tail lights won't turn off

To check Mr. Turcotte's suggestion, turn on the car and have someone observe what happens when you step on the brake pedal. If there is no change, the brake light switch is stuck on or its contacts are welded. It's mounted on the brake pedal mechanism under the dashboard (usually it's a small box with two wires going to terminals on it, and a plastic peg switch actuator that is pushed in by the the brake pedal lever. The peg should go in when you push on the pedal, and come out of the box when you let up on the pedal).

If the lights get brighter or more lights come on in the back when you step on the pedal, the problem is a shorted light switch or relay, or a fault in the body controller computer that is supposed to automatically turn off the lights shortly after you leave the vehicle.