Was the recall ever done on that cable? it was #970 to replace the cable because the cable end would fray and stick where it would feed back into the tube. When they done mine they replaced the cable and the linkage to the pump. Has worked perfectly ever since.
Don't think I would use oil for a lube, attracts dirt and will gum up. Maybe a dry lube and work the lube into the shaft housing.
Use the process of elimination cause there is a few joints to eliminate.