Relay problem, I think. Where is it?

Probably not a relay. My 01 tt roadster had same problem. Its a computer chip located behind center of back. $800 tepair

You've probably got a water-damaged computer. Very common with convertibles. It's behind the passenger seat, under the tray that the top folds into. While the top is up, there's a flip-up section of the tray where you can see the culprit. It's also accessible somewhat from the trunk if you pull out the box thingy way in the front. Disconnect the battery (make sure you have your 4-digit radio security code first), remove the computer assembly, clean the contacts where all the plugs fit, and pray a lot. New computers are over $1000. While you're in there, clean the side water drain holes and verify the window is really sealed to the folding top. If you see 2 similar-looking computer boxes, the front one is your Bose power amp and the rear one is your culprit. Lots of good how-to articles on the Audi TT forums. Good luck.