Rear weeper – electrical question

[EE80Liftback]

Yeah, having a wire that's live if the ignition is on is normal, as it allows the wiper to return from half way the windscreen back to its rest position after you switch it off!

Of course when you switch it on, one more wire should become live, so that all sounds good.

So, if your ground connection is also fine then it sounds like the motor is dead (I don't know much AE86 specifics, so don't know if there's a ground wire or whether its just a metal motor screwed to a metal part of the car, but anyway, you can figure that out yourself).