After many months of searching I found a factory remanufactured OEM wiper motor for my 1960 on Ebay. They do turn up infrequently. I’m not aware of anyone that rebuilds these and makes them generally available. Also note there are two different styles of motors on the 60-66 – one mounts parallel to the firewall, and the other points toward the back of the dash. Just check which type you have before shopping for a replacement.
An alternative is one of the new design wipers systems from Newport Engineering. Back in the 1980’s I installed one in my 1946 Ford and loved it. Worked perfectly, self parking, and two speeds. They also sell a delay switch for it.
A few years ago my son installed one of the Newport systems in his 1960 Galaxie and hated it. High speed was slower than his original vacuum motor, and slow speed wasn’t even worth using. So I don’t know if their quality has diminished, or my son just got a defective unit. I sure did like mine. I’d probably put one in my truck, but it is rarely driven in bad weather any longer, and I also can’t afford it.
http://newportwipers.com/products.php?year=1960-66&make_id=2