READ:
http://tss.likeabigdog.com/On the non-grand prix lines, the brake lights might not work due to a bad TSS(turn signal switch), in addition to the hazards not working right, but that should not be your issue.
the ground issue mentioned most likely only affects the intermittent issue and not the brake lights since all your other rear lights work, if I understood what you said correctly
Please take the time to check every fuse to make sure none are burned out, and that all are in the correct spots... I fixed a S10 that had a exterior light wire ground out, popping the fuse, and when it did it turned the interior lights on.