Mine does ('63). I don't have access to a wiring diagram but there is just unswitched current going to one of the contacts on the motor - and a set of contacts inside the little gear case that only open in the parked position. With the key on and the wipers off, you should have 12V+ on one of the terminals on the motor - if not investigate why. If you do, and the wipers aren't parked then something is amiss inside the gearbox with the contacts.

That 12V+ should go off whith the key off - my first car was a '63 VW Beetle with the highly dubious feature of parking the wipers even with the key off. Of course, if snow packed up underneath the wipers (But wouldn't the defroster melt that off - AHAHAHAHAHAHAHA! No.) then when you turned the car off they would strain and struggle endlessly to pack the snow down and park. Until either the battery went dead (the good scenario) or the motor overheated and died (the bad scenario).
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I'm JohnMc, and I approved this message.