One thing to try when they don't work is to measure for the presence of voltage on the case of the wiper motor. Alternatively, you might get it to run by pushing on the motor. If you find voltage on the case, there is a bad ground. The whole thing is mounted to a plate on rubber isolators to dampen vibration. There is a brass ground strap riveted to the plate and it goes under the head of one of the three mounting bolts. That's where it burns a spot that causes the bad connection. The best and permanent fix is to attach a ground wire to the plate and to the body. Some older motors had five screws that held the black plastic switch plate to the motor's gear assembly. You can attach a wire to one of those screws. On newer models they used rivets instead of screws. If nothing else presents itself, you can drill a hole in the plate and run a self-tapping screw in to attach the wire.
If you do not find voltage on the motor, (remember, the wipers must be turned on to low or high), check for voltage on the wires in the electrical connector. I'll have to dig out a service manual because they took a simple, reliable circuit that I had memorized and added a complicated computer to it.