You may or may not see a drip on the suction side. It only takes a very small leak to let in a lot of air. One thing for certain is it has to be on the suction side. As for the gurgling when the pump is shut off, could be the same leak or a valve letting air into the system from the waste line. Don't know what kind of valving arrangement you have and not that familiar with DE filters but if it's a multiport valve it could be the valve gasket. With the pump running is there any water coming out the waste line? Even a small dribble? Also remember the gurgling may, and probably is, a totally separate issue from the air getting in.
Al
Edit: And a big welcome to the forum.