the connection between the battery and the brake lights
Headlights? Brake lights? Tail lights? Signal lights? Courtesy lights? Dash lights? Check engine lights? Need more info please.
Check the brake light fuse. If you have 12 volts at the brake light switch I would suspect the signal light switch is at fault.
The head light switch is shorting out ,or a bad connection
There could be a severed connection somewhere along the line, or it could just be a blown fuse
Check the ground wire. You have a bad connection somewhere.
The brake lights and tail lights are separate wiring systems. Even some of the bulbs may have two separate bulbs in the same glass housing. If the bulbs are in fact working, then the next step would be to test the brake switch under the dash. When you depress the brake pedal the switch is pushed creating a connection to turn on the brake lights.
Look at your brake pedal where it connects under the dash. The problems you are having are both related to the brake pedal. There is a safety feature that won't allow you to shift your tranny until you have applied the brake, and since your brake lights are not coming on, there is either an electrical connection or a mechanical connection that is not working.
The tail light/brake light bulb has two filaments. If one of the filaments is broken, you will get either only tail lights, or brake lights. If a new bulb doesn't work, then you have a broken wire or bad connection in your plug-in.
It can be connection wires, bulbs or fuses.
The tail lights and the stop lights work off of different circuits. The stop lights work when the brake pedal is depressed while the tail lights work when the light switch is turned on. Look for a burnt fuse or a bad connection.
First things first you need to check your fuses. In the owners manual you will find the location of the fuse that relates to the brake lights. Take the fuse out and hold it up to see if the connection is broken if it is replace and the brake lights should work.