89 Wrangler windshield wiper control arm / blinker arm broken off. I can stick the stub end of the arm back in the hole and make the blinkers work but not the wipers. How does this arm control the wipers? Does the arm stub need to be pressed into the hole? It looks like it slips inside...round stub / round hole. Do I need to replace the whole thing?

SOURCE: 1998 Jeep Wrangler Electrical Short in Steering Column?

I had a similar problem with my 2000 Jeep TJ and I found the problem in the wiring harness under the hood.several wires were corroded and almost burnt off.If you remove the black tape which keeps the harness bundled together and if you see evidence of "green" type powder or "gook" it's most likely where the wires have faulted.

SOURCE: fuse box

Under the left of the dash board close to the parking brake tucked up under.

SOURCE: right blinker stay on when key is on blinker arm want cut it off

happened in my 1997 dodge avenger, go ahead and replace the complete turn signal behind the plastic on the columb, very easy to do, 3 screws under the columb, 2 screws on the black plastic side of the turnsignal swithch facing the drivers side door, unplug, put in new or one out of junk yard, thats what i did and it fixed no problem...

SOURCE: Wipers come on when blinker is turned on and won't go off

Motherboard?

I think it's a problem with the wiring harness. Probably have a short somewhere.
In reality, things like this, with american cars, it's pretty normal.

I had a ford taurus once.... it was full of electrical and mechanical faults.

Consult a dealership, they could do some troubleshooting.

SOURCE: Windshield Wipers dont work and can be moved freely by hand

sounds like wipers arm is not securely attached to shaft that is attached to wiper motors. They can strip out and you can either us JB weld to put them on or get new ones or junk yard ones.