Both rear brake lights stopped working. What could be the problem/what do I check?

 

Moved your post to correct forum for help.

Fuse 30 in under hood fuse box controlled brake lights on earlier models. Check this first.

Are you having problems getting shifter to shift from P to D? If yes, then look for brake light switch on brake pedal to be stuck in open position (does not extend when brake is pressed).

Sometimes a good dose of WD40 and manual exercise will fix. Otherwise a new switch is indicated.

good luck