Probably an improperly adjusted brake light switch, or a defective switch. The switch is a simple device mounted to the brake pedal - easy to check and easy to replace.
No , the rear brake lights do not turn on when you use your parking brake , just the brake light on your dash is supposed to come on
No they don't.
the turn signal switch is probably bad
Generally brown is used for running lights, green for right turn and brake, yellow for left turn and brake.
the ground for the rear lights is by the radio aerial inside the rear passanger side wing.
change the fuse if not replace flasher
The brake lights and all of the rear lights can be access through the inside back molding in the rear. there are little knobs that you turn to access them.
blown fuse or turn switch bad
It's the turn signal switch which is the culprit.
Blown fuse? Bad stoplight switch? Open wire to brake lights Not ground at brake light sockets? Problem in steering column (turn signal circuitry)?
Try checking the tail light relay.
check for a loose ground wire