If a brake light stays on it's usually just a sticky or bad switch. The brake light switch is under the dash and is activated by the brake pedal. It could have some grunge on it preventing the switch from closing. Try cleaning the plunger. If that doesn't work (and it probably won't) replacement is very easy.
Cheers
Any light that stays on is not a "brake light", it's a "tail light". It's possible that they may be on at a lower level normally, and brighten when the brakes are applied, though.
emergency brake light stays on
Warning light usually indicates low brake fluid or parking brake not fully released
Defective or misadjusted, brake light switch.
The battery light stays on when the alternator is over or under charging. The red brake light stays on when the parking brake is set or the fluid is low. The abs light stays on when the abs computer detects a malfunction and sets a code.
brake light swith located under the brake pedal is stuck.
The brake lights work without the key on, so you have a problem with your brake light switch.
no
brake light switch is broken or out of adjustment. brake light switch is located above brake pedal.
If you are referring to the brake light then the brake light switch is stuck.
With an ohmeter or a self-powered test light. Hook the two leads of your tester to the terminals on the brake light switch. Push down on the brake pedal and if the light stays off or the meter stays at infinity, the switch is bad.
check brake fluid