Before changing the flasher relay i'd check the hazards switch. The turn signals, high beams and emergency flasher all go through this switch.
I havent got my MK2 any more so cant check a car but i checked the Bentley wiring diagram for 1990 golf diesel (p198) and it says there should be 3 sets of wires going into the back of the switch. You said you havent got a copy of it so heres the details:
One connector with 5 wires together (4 to high beams/headlights, one to flasher relay= white/yellow) red/yellow= power from main circuit 30/constant live, white= down stream of switch power to high beams and the blue dash light, white/black = power from headlight switch, yellow= downstream to headlights.
2 wires from L and R turn signals (blk/green and blk/white respectively)
2 that connect the switch to the flasher relay (blk/blue= power from switched main circuit 15(ignition on live) via fuse 17 and black/white/green= switch to relay and dash instrument light)
Best bet would be to swap it with a known working switch. Do you know anyone you could borrow one off?
Failing that try this:
Power looks it comes from either red/yellow (30), white/black (headlight switch) or black/blue (15 via fuse 17). I'd try removing fuse 17 and see if the two dimly lit lights go out. If they do the parasitic circuit is coming in from here and feeding both lamps via fault in the switch. Same again by removing the 5 wire connector - it should only carry current to the high beam circuit so if both dim lamps go out this is the source of the problem and the power is going where it shouldn't inside the switch. Jumping red/yellow and white wires off the 5 wire connector should then get the high beams and the blue bulb to light in the dash, thereby hopefully proving we havent disabled the circuit in some other way that'll skew the results.
If none of this makes sense pm me your email address and i'll scan the diagram and send it to you.