This might sound too obvious, but the only reason to tighten your grip on the pole (with either hand) is so that you don't drop it. You should experiment, and hold it as lightly as you can without dropping it (or losing control/balance of it). The looser the grip, the more relaxed (and faster) you'll run.
During the first half of the run especially, an open grip with the top hand (the hand nearest the top of the pole) allows you to carry it more upright, without feeling awkward.
During the plant, you want the pole to pass as close to your armpit and ear as you can. You want to plant the pole "THROUGH" the shoulder. An open grip in this phase is always closer to the shoulder than a closed grip. So even if you grip it tightly during the run, you should loosen it during the plant.
Once you clear your shoulder, you of course need to tighten your grip to hold the impact of your body weight. Many vaulters are afraid of tightening their grip like this, at the last second, for fear that it might not be tight enough on impact. In practice, this is rarely a problem. If you do lots of gym work - and you should - (rings, high-bar), then you should have the confidence in yourself that you're easily able to hold your body weight with the top hand. If not, maybe you need more gym work.
I recommend that you focus on keeping your plant tight to the shoulder with an open grip. How you hold the pole during the run is only secondary to this - but an open grip during the run more-or-less sets you up for a good open grip during the plant.
"The sky's the limit!" - Bob Richards Sr. - PV Gold Medalist 1952 & 1956 Olympics