If you cannot reduce to a drip then the pump might be so far out of time it will have to be pulled and moved to the next spline or so. Rotate engine bottom pulley until you just get a drip. This will indicate the correction direction to move the pump spline if required. A pump will not usually go this far out by itself.
It would be advisable to try to get an accurate chain stretch estimate before proceeding as well. Since the pump only rotates a given number of degrees in its slot that chain might be really stretched.