could it be the wire sizing being too small now that you have more power wanting to go to the tail lights or your ground wire you used is too small for it to return?
i have a 93 tsi as well, mine also has this issue, i am sure it is the tumblers worn from x amount of times it was used, needs a new lock on driverside
had this issue with my car, the secuity key has contacts deteriorating and would make the noise, battery was new, terminals all cleaned, grounds all taken off and sanded to make sure, and after soldering it car starts great everytime