Have you checked your brake fluid?
check brake fluid level.
fault brake light switch, located at the top of the brake pedal.
check brake light fuse and brake light switch on pedal
why my jeep brake light on all time
Try checking the switch in the hand lever itself. Sometimes it can get a piece of trash stuck in it.or it can be worn out. On a 93 escort the parking brake light also doubles as a low brake fluid warning light. It may be the same with a 2001. So you could have a leak somewhere.
Probably the alternator. Have it checked if it is charging.
The brake fluid may be low. If it is low, it is a sign that you are in need of brake work soon.
check your brake fluid levels
Check the level of brake fluid in the master cylinder reservoir. If it is low that will illuminate the brake light also. If it is low on brake fluid it's time to have the brakes serviced.
Check your brake fluid, it more then likely is low. That is a good indicator when the light comes on, if its not that... you might want to check your Ebrake cable underneath the car make sure its not hung up.
A malfunctioning brake light relay switch will cause your 1993 Toyota Corolla brake lights to stay on all the time. The brake light relay switch is located beneath the drivers side dashboard.
check the brake fluid level in your master cylinder under the hood. The light comes on for two reasons, either the hand brake is on or your brake fluid level is low