I would start with the relay, since its easy. check out me fusebox faq to figure out which one it is

next I would try another stalk, just need to get the wheel off (24mm nut, 2 allen bolts on the back if it has an airbag) and its 3 screws holding the stalk on. If that doesnt help then look at the wiper motor itself, bit of a pain to get to on a mk3 as you have to pull the scuttle trim off, which means the wipers have to come off as well

My rear motor did pretty much the same thing, ran forever and stopped when it felt like it, turned oput to be the motor at fault. Actually if you listen to the relay, you should hear it click when it wants to trigger the wiper, if its not clickign but the wipers are off on their merry way you can be reasonably sure its not the relay.