Check all wiring connections. If good, likely problem is inside the wiper motor. There are 2 power circuits, one to operate wipers and one to park wipers. If you bang on the motor with key on and the wipers park, that verifies it. My '66 does the same thing. I assume there are contacts in the motor that can be cleaned.

It's a '66. Thanks guys. I'll do some investigative work.

Just went through the same thing.  thinking the motor was bad.  After taking the motor out and bench testing found the motor was not the problem.  Switch was bad.  I would recommend replacing the switch if all the wires ohm out correctly before pulling the motor.  Pulling the motor and assembly bracket was a challenge at my age.  If you are young and limber it might not be so bad.  I would only pull the motor after checking everything else.  the switch should have a 2 wire 12 volt circuit and a 2 wire low voltage circuit.  The low voltage is what parks the wipers.  I am referring to a single speed motor.  2 speed is more complicated;but, the same principal.  On the single speed you pull switch knob to provide power to the washer pump.