Think about why there are two lumens in this tube. Imagine there were just one, connected to suction. When the fluid is all drained, or there is very little accumulating, the suction keeps...sucking, and will pull on the lining of the stomach, resulting in damage to the mucosa. This is, in fact, why that air vent was invented: to break the suction and prevent mucosal damage.
So, knowing that, you can see why you NEVER clamp off the air vent when the main lumen is to suction. You'd be defeating its protective purpose.
There should always be air going down the air vent lumen (listen or feel it with your fingertip briefly), and fluid or at least air coming up the main lumen. If either of those is not happening, it's your job to investigate and fix it.
If fluid is coming up the air vent (a common cause of inappropriate clamping) it's because, well, air isn't going down it, probably because the main lumen is obstructed and there's no suction pulling air down the vent. To figure this out, IF there is no contraindication to moving the tube a bit, irrigate it with a bit of saline and /or withdraw it a few inches, move it up and down. Chances are it will suddenly start to drain and the air will start to go down the air vent. You can push a little air down the vent to clear it. When you have it draining properly, re-secure it.
Be prepared to do this often. These things will occur regularly. Ignoring them, defeating the safety feature of the tube, or just saying the heck with it is risky for your patient and defeats the purpose of the drain being there in the first place. There's a reason it's there: make sure it does what it should do.
If you don't clear the main lumen AND you have clamped the air vent (because it's making a mess on the pillowcase) you now have NO suction to the stomach, and when enough fluid builds up the patient can aspirate. This IS dangerous.