My '66 did the same thing. It was just a loose wire on the back of the switch IIRC, then all was well.
UNTIL a body shop stopped them in the up postion to remove them, and put them back on in the down position. Unfortunately the shafts were still in the up position however. So the first time I turned them on they tried to go down and just overextended them down on the cowl
scratching the paint and breaking a spring in the passenger wiper arm.