How do you replace brake light 1996 cadillac deville

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.

Replace the brake light switch (bottom of steering column on brake pedal support)

Check brake light switch, on back side of brake pedal
arm, under dash

most likely cause is damaged wires in the rubber boot from body to teh tailgate

there is a switch under your brake pedal that activates your brake lights when you push the pedal, it sounds like the switch is stuck in the in position

I would call the Cadillac dealer, he can help you.

Front brakes on all modern cars are disc brakes. The front brakes generally provide 80% of the stopping power, and so tend to wear faster than the rear. Replacing them - pads, rotors and calipers - is quite simple once you understand the process, and can save you a great deal of money. These instructions will include a full front brake replacement. Also, having a service manual for your vehicle will save your sanity, as well as time and money. If you only need pads, or pads and rotors, but not calipers, skip the steps for replacing calipers. Repeat the steps below for each side of the car as necessary.
Complete Directions

Look for the wires leading to the light on the 2000 Cadillac Deville.
Try to figure out which one leads to the 'white' light that is for backup.
If there is a replaceable bulb, then there should be a way of rotating a socket out from behind.
Some Devilles have LED lighting for the red brake lights, I think.

I would suggest checking your Oxygen sensor which will light up your service emission light. Check that and let me know Good luck

remove your license and behind it you will find i think two screws then remove that panel and you should be able to get to it.