I have a 69 TBird that has/had the same issue. I'm sure you know it is a Hydraulic operated wiper motor and mine also has intermittent positions in addition to On/Off. The first thing I did was to take off the wiper arms to keep them from dry wiping the windshield.
Mine was sitting for 35 + years. First thing I did was to add about 3 - 4 oz of Seal Lube. ( read up on it. I use it religiously. ) I know some will say never use it, but it works for me. Then run the engine until Hot, and turning the steering wheel stop to assist in getting the air out of the system, let the system run. I did 30 min. It may work itself out with lubing up the internals of the wiper motor. As you can turn your knob your cable is most likely moving the actuator by means of the cable (on/off/position) arm on the pax side of the wiper motor. You may need to run teh engine a couple times to get the seal lube to work on internals. ( I did three times )
Next step if that does not work, take the hydraulic lines off at the fire wall and remove the roughly 8 inch by 3 inch access panel held on with 4 1/4 inch screws. You will see the actuating cable on the front of the wiper motor held in place with a single small screw. Have someone move the switch on the instrument panel and see if the cable is moving the actuator arm on the pax side of the wiper motor. If it moves, that's good. IF actuator arm does not move the cable is probably rusted and after weeks of attempting to loosen mine, I have not been successful. I unhooked the cable from the actuator arm. Careful as the cable slides into the actuator arm from back to front and there is a small washer like retainer on the end of the cable. With a needle nose pliers you can push from the front to back to slide the cable off the actuator arm. Then you can manually move the actuator lever/arm from left to right. A bit further back and on the body of the wiper motor and arm is a small steel ( I think ) button, similar to like what you find on a
carb diaghram. Then I used the special wiper motor tool (flat blade screwdriver) between the arm/lever and wiper body to work the button and make sure it is free. It will mover ever so little and it is really hard to see any action where it is.
I was able to loosen mine up and run the wipers by hand (fingers) moving the lever. Off is full to the Pax side. (best position for removing the cable) If you can make the wipers run on and off, you probably wont have to remover the wiper motor. if you have to that would mean the lower windshield chrome, and cowel to gain access to the mounting bolts for the wipe motor. In my case the cable needs to be replaced and in the meantime I reconnected the hydraulic lines and put a small wedge between the wiper motor and actuator arm/lever to off position so I can run the engine without the wipers being On.
Sort of a long explanation but I had to learn on my own as there is little to No info available I have found anywhere. Even the shoppe manual is vague. So, If anyone had more or better info, I too would love to hear about your remedy, especially the next
part for me it the removal of the control and gauge from the dash / instrument panel.
The attached drawing shows the 69 on the bottom half of the page and no where does any FORD drawing show the details of my explanation, nor are there any videos.
