Could be the flasher unit.
There are two flashers, one for the hazards and one for the signals.
check your ground wire in the back
check the fuse first!
I replace my flasher fuse.Now they light up but won't blink.
replace turn signal flasher, hazard flasher is separate
The 1990 VW Jetta turn signals will not work when the ground wire is broken or corroded. The turn signals may need the lightbulb's replaced.
Most likely a bad turn signal flasher or blown fuse
have you tryed all the fuses then check if the bulbs are good
If the turn signal bulbs light but will not flash, the flasher relay is defective, replace it.
replace flaser can in fuse box
If the turn signal lights come on but will not flash you have a defective flasher relay. Replace the relay.