Kat, I know this is going to sound silly, but have your recently replaced any bulbs in the car? Sometimes if you don't get them installed just so, they can short between two contacts inside of the bulb base, leading to some strange happenings. Specifically, I would be looking at the inside bulbs of the rear tail lights since this seems to be related to the brake lights.

As for fixing the issue. I would tell you to remove the panels off of the tail lights and lay both panels on the floor of the trunk with the bulbs removed. Now, with the key in the RUN position, press on the brake and turn on the turn signal. Do you get the same issue? If yes, then odds are you GEM module (GECM) is bad. Ignore any message about light bulbs being burned out. If the problem is clear, then install 1 bulb and then try again. If the problem returns, the bulb that you just replaced has the issue. Let me know which bulb it is and I will see what I can find from there. If the problem does not return, add another bulb and repeat until you get all the bulbs in. If you can get all the bulbs in and the problem doesn't return, then it was simply a bulb that was not seated correctly.