Must be a common situation, because I have exactly the same problem, also with a 2001 TDi.
Now, what's not clear: is the price (and part number 8Z0 etc) mentioned that of the whole flasher unit, that can be installed by simple replacing (and not the soldering stuff explained in the link)?
Moreover, VAG parts doesn't seem to have it? So I can only get hold of it at the friendly dealer's?