Check switch under pedal & make sure is turning off when not applied.
Brake lights draw their energy from the vehicle's battery.
The head lights are the biggest long term drain on your battery. (The starter is a heavier drain, but you can't leave it on for very long.)
the connection between the battery and the brake lights
you drain your battery when you leave your lights on
You probably have a bad ground. Check the grounds on the brake lights.
The brake lights will stay on if the switch is either out of adjustment or damaged. Pull up on the brake pedal to see if it will go out, if it does, you might be able to get by just adjusting the position of the brake light switch. BTW, it's on the brake pedal mechanism, under the dashboard.
Do you mean What does it mean when the brake and battery lights come on in when it is already started? Check your alternator may be its not working well it cause the battery sign comes out.
that keeps the dome lights on
"Stuck" brake lights indicate that the brake light switch on the brake pedal is broken. It should be replaced.
Battery dead
Yes, if your car sits a few days at a time and your cars interior lights periodically come on it will drain your battery.