Im having the same problem on my 01 epxedition, How do you get the motor itself out? It looks like its held in by rivets?

 

You dont need to take it out to test it, but if you are wanting to take it out I'd take it to a dealer. There is a lot of pressure on some bars or soemthing in there (not really sure what but Haynes manual warns you bout it) One of friends took his to dealership and it cost him $300. I took it to local mechanic, cost $181 and it took less than a day in and out. Course I did tell him to replace to motor, I didnt tell him to find the prob, just said replace motor, because I was confident that was the prob. He replaced it, been fine since.

 

Mine does the same thing, but my wipers also quit. Found that if I wiggle the relay, it starts working again. I have replaced relays twice. It just seems to get loose in there.