My experience with this problem especially with the Rabbits and that group(water cooled fwd) is that the bulbs are not very good. Try your emergency flashers. Do they work? Go outside and check the bulbs? Are they all working? If they are, chance are that, if you shut off the emergency flasher and hit the signal switch, they will work. If the signal lights does not work, then it is in the control arm behind the steering wheel.
When doing the 4way emergency flasher thing and you see a bulb out on one side. Turn off the emergency flash and try the signal on that side. What it tells you is that it doesn't work with a dead bulb.
The bulb sockets are loose fitting and get corrodded. Need to sand it clean of rust and then put a good bulb in. With the signal light cover off(if you can do that kind of thing) see if you can move the bulb while the flasher is going to see if it can jiggle the bulb out(not working) as though you hit a bump in the road. You see what I am trying to say is that they don't fit good and if you can figure out a way for the bulb not to move, then thelight will not go out and the signal will continue to work on that side.
The 4way hazard works whether there is 4 bulbs working or 3 or 2 is working.
If you decide it is the flasher unit it will be in the fuse box. Hopefully it works enough so you can tell which relay it is (could be square plastic or a silver box) Go with checking the integrity of the bulbs and their sockets first.