I'd check the sensor for the emergency brake. It's probably faulty.
I've got a '92 skylark, and had a problem with the brake lights staying on even after the car was off. There is an adjustment that is connected to the brake pedal that you can adjust the tension on. It's kind of a pain to get up under there unless you're skinny though.
Loose contacts or your sensor may be stuffed - see an auto electrician
The 2001 Buick Century brake light switch is located beneath the dashboard, on the drivers side. The brake light switch should be labeled as such.
check obd2 with scanner for trouble codes find problem, fix or replace sensor or part, clear codes with scan tool
Check taillight/parking light sockets for corrosion short to ground
I have 05 with no brake lights
you have a brake problem and need to have it repaired before you can reset the light sensor you have a brake problem and need to have it repaired before you can reset the light sensor
if it is in the back window like im thinking it is get in the trunk and you should be able to see the wires going up it and it will either plug in or you can unscrew it and replace it with the correct bulb
Check the sensor on the brake pedal arm.
There is a brake fluid sensor located in the reservoir at the master cylinder. When the brake fluid is low it will turn the light on.
Most likely there's not enough brake fluid or your master cylinder is ready to give out.