Do the hazard lights work? Everything routes through that switch. I've
seen a bad flasher cause that problem too, it's on the left side of the
car, behind the lower center console to the left of the heater control
slider.

Check that the 4-way switch is not partially engaged.
This happed to me, once.

Switch it in and out. That should do it.
If not...

I have also had the wiring connection loosen up on the column.
One screw loose.
Check those.

Steve

Clean the ends of the fuses and the sockets. They sometimes get
corrupted and won't make good contact. The silver tipped (zinc plated
steel) fuses are the worst. Get the copper tipped ones.
Check the relay behind the left side plastic console cover. You can put
12V to it and make it snap shut.

On my '83, the relay gets flaky. When it's cold out, the blinkers won't
blink. I can whack the side of the console and they will blink. One
whack, one blink.
Once everything in the cabin warms up, they blink fine.
I pulled the relay and flowed all the solder joints. Didn't help. I'm
guessing the coil is weak and not pulling in like it should. It works if
I leave the plastic cover off the relay. Snap the cover on and it stops
working.
One day I'll replace it.
It's a bit annoying hearing the relay clicking randomly while driving
down the road though...