Brake lights on rear of car will not work

Try swapping them out with new ones. If the third brake light/collision avoidance light is working, that means the switch is working. Check the grounds and the connections at the brake light pigtails.

That is usually caused by a bad turn signal switch. The lower two brake lights pass through that switch so the turn signals can cancel the brake lights when necessary. It really should be tested in and out of the switch before changing anything.