It might be the needle bearing. If it leaks, bubbles of air can be sucked into the body and cause pulsing. If that's the case, it won't happen if the airbrush is held upside down, because there will be a slight pressure rather than a vacuum in the body. Or, you could put some water in the 1/4oz cup and tilt the airbrush to the right so that the water level is higher than the body. If the problem goes away, it could be the bearing. Do you feel a little drag if you pull the needle out?
Another possibility is a slight leak where the cup fits into the body. Does it do it with both a cup and a bottle?
Don