Sounds to me like a screwed up set of contacts in the wiper motor. (edit: stuck in 'park')
When the wipers are switched off, there is a set of contacts that maintain a path to ground while the wipers 'park'
This sets off another reaction that actually "parks" the wipers. Actually it kinda activates a cam.
Pretty much all of these motors work the same, the hide-aways most likely just use a different cam to park them.
If it is a 'new' motor, it is most likely a rebuilt motor that has set on the shelf for quite some time and the contacts have some 'crap' on 'em.
Same thing happened to me. the vendor I bought the motor from had it shipped from the rebuilder. Wish I could remember his name. He kinda explained to me what was actually going on. He even walked me thru the fixing to get me going 'til he could get another out to me.
He sent me a new motor on the 'honor system'. He just asked me to return the first unit upon delivery of the replacement.
When I get home I will see if I still have his number somewhere.