It definitely sounds like a relay, likey ou said. I wouldn't have pegged it on the underdrive pulley, but it does make sense. When you turn the car on, it sends power to the relay, then "flipping two switches" internally. If there isn't enough power to "flip the switches" then it won't come on, yet after charging up for a few minutes, it would... I'd get rid of the pulley to see if that fixes it... Try turning the car to on, but not starting it. If teh fan doesn't come on, I'm guessing it's just the relay. If it does, then your guess should be correct.