I called Audi, and they do not acknowledge that this is a widespread problem. It's ridiculous that they won't stand by their product. This is clearly a poorly engineered design.
My 2008 Audi TT would constantly beep with "Right Rear Light" or "Left Rear Light" with an X through a light bulb symbol popping up on the screen in between the tachometer and the speedometer. If I applied the brakes, the X through a light bulb symbol would go away. It turns out that the light that is farthest outboard in the tail light housing (on both left and right sides) was the problem.
I used this video to remove the tail lights:
http://www.carcarekiosk.com/video/20...hts/tail_light
They can be a little difficult to pop out because you have to push/pull to the side, not directly out.
I found that the problem was with corrosion within the connectors that go directly to the tail light housing. It appears that one wire is much larger than the other wires, but the size of the connector is the same. The wire has too much current for the connector to handle. It melts the plastic around it and becomes corroded as a result. I scraped the corrosion off with a tiny screwdriver (as recommended above), and that fixed the problem for about a month. So I did it a second time, and then used the ends of plastic zip ties to apply pressure to the connector so it wouldn't become loose. It has been about a month and I haven't had a problem.
I attached pictures below so you can see the problem.
I am so beyond angry that Audi won't stand by their product. These are expensive cars, and we pay more money because they are supposed to be well-engineered and fun to drive. It is very difficult to enjoy the drive when my car beeps loudly every time I release the brake.
I hope this post helps someone. I apologize that I probably don't use the proper car "lingo." I'm just a regular person trying to not pay $90 for the "diagnosis fee" and $450 per light that the dealer wants to charge. This is such an annoying problem.
And kudos to my uncle that pretty much helped me through the entire problem. He's the real genius here.
Images: The brown wire is much larger, and the one that has the corroded connector:
The top right connector is corroded and melted on the right tail light:

And the corresponding connector to the right tail light housing:
And the same issue on the left side, for the left tail light:

And the corresponding connector to the left tail light housing:
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