My Keystone Outback had the water pump located on the drivers side of the trailer, beside the bed, under that carpeted box beside the bed.
I looked at some photos of your model and that box looks like the spot!
In order to open mine, I had to raise the bed. The top of the box was screwed down, and the screw heads were hidden in the carpet. But I found them.
I unscrewed them and then the top lifted off like a lid. The carpet itself was the hinge on the front side, so it raised from the back. When I put it back, I never put the screws back in so I could open it easier. But the bed had to be raised to do so.
Check there. Cougars and Outbacks are both Keystone campers, they are made similar. The water pump is going to be very near your fresh water gravity fill port. If your water fill is right outside the wall from that box, then that is were it's at.
