Why do my brake lights stays on my 08n dts - 2008 Cadillac Dts

check brake light switch first if all 3 lights are out-- located under dash at brake pedal bracket

shift interlock system solenoid ? Doesn't gear selector move from park ? DTS ???? Cadillac ???? If it is the cadillac dts , brake pedal position sensor is a input to the BCM - body contol module . The BCM controls the shift lock control solenoid . Your best bet , take it to a qualified repair shop.

The first thing you do is check the brake lights, do they work, if not you found your problem.

The light being on means the system has detected a problem in one or more sensors. The vibration is the ABS modulating the brakes to prevent skidding because it has detected a wheel that is locked up. That wheel is most likely the one sensor that is giving you the error.

The stability control system is typically triggered by the abs system/connector sensor on your wheel hub bearing. If you haven't replaced your hub bearings on the front you may have one going bad. Cheap fix for a diy.

Ok short in bulb or socket causing backflow of pixies through brake filament to ground. Next.

switch is bad

If all three brake lights are on, I'd say the problem is in the switch by the brake pedal. Take the cover off below the steering wheel and inspect the brake pedal and the switch. It may be as easy as spraying some silicone lube on the actuator. Try to do a search on this forum for brake light switch.