It doesn't work for me. ('97 A4 Avant 1.8)
The first procedure you wrote is not good for me because if I pull (cannot be pushed) the LEFT button (from the clock) - it adjusts the clock even without the key inserted.
The alternative procedure doesn't work. I have tried to switch the key to ON position (when all the lights turn on), but without starting the engine. Do I have to start the engine?
What I did:
I pressed the right button (the one close to the km counter display). I turn the key to ON position, and in the trip km counter the text 'IN 1' appears (I understood this means Inspection Required). I then tried pulling the left button, but nothing happened. The text dissapeared as usually after a few seconds, and appeares again at the next start.