it definitly isnt the relay, so you can skip that. if the indicators work fine one way, the relay is ok

I still recon its the stalks, but it could be dodgy wiring from them to the back of the fusebox. trouble is on a mk3 access is poor, even if you remove the dash under tray, thanks to the kneebar that runs across under the dash. pull the under tray out and the lower ignition lock shroud plus the wheel and stalksd, this will give you better access to the wiring. check it for any obvious damage or shorts, and look the indicator stalk over for damage and loose pins. Make sure the hazard button is clipped on the back properly as well. Give it a good clean and check the contacts for dirt, then reassemble it all and try again.
a 90spec MK2 (hazard on column) stalk will swap on, though the shrouds probably wont screw back on, fine to run it without to get you motoring however. MK3, Corrado, Passat and SEAT stalks will fit as well. pretty muich anything with a hazard switch on top of the column! be aware polos look right but the wiring on them is a bit different sometimes.