The 2001 Chevy Blazer brake lights may not work and the third bake stays on because the current light needs to be replaced. A replacement brake light can be purchased at an Auto Parts store like Pep Boys.
A third brake light is used to provide a deceleration warning to vehicles that can't see the left and right lights. You can learn more about these brake lights at the Wikipedia.
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.
I assume you have checked/replaced the bulbs. Take a cicuit tester and check the wire harness connections under the bumper and around the trailer connector if you have one. The problem must be at that area IF all your other lights are working as you said.
this tells you is a simple wiring problem.most likely a loose wire from the third light to the other lights.(third lights provides the power to the other lights)
wrong bulbs or bad earth
it would be the brake light switch about 20 dollars at autozone
Fuse for the "Third" Brake LightAlthough I have no experience with the Chevy Tahoe, the systems are similar for almost all vehicles.The third brake light is tied into the wiring for the other brake lights and is protected by the SAME fuse they are.Thus, there is no separate fuse for the third brake light.Therefore, IF your other brake lights are working, then a failure of the third brake light to activate IS NOT caused by a fuse, but instead an "open circuit" condition in the "dedicated" third brakelight wiring [from where its wire "splits" off of the wiring harness to the other brake lights].This is usually caused by a connector which has become disconnected, or a cut or broken wire.
The third brake light is named for then Secretary of Transportation Elizabeth Dole and are called "dole lights".
Chevelles never had a third brake light since the Chevelle name was dropped after 1977. However, third brake lights were first installed (and required) in 1986.
Check the bulbs - they are double filamented- smaller for stop and larger for tailights
New bulb needed or broken wire
Yes, it is the same fuse used for the rear brake lights.