Gas cap confusion

For the ‘65 Valiant station and Barracuda I am in need for gas caps. As the Valiant lives on the street I would like a locking version on that one.

Now here is my confusion: I see the gas cap of damraider and I see the Stant locking gas cap, both of which are NON vented. Now, when I drove back the Valiant home, with its original gas cap on, at one time after refueling I tightened it a little too much. After a while the car started running horribly (way too lean) and the fuel tank started leaking, all of which stopped when loosening the gas cap.

So how does a non vented gas cap work on a ‘65 Plymouth a-body? How does the tank vent with a non vented cap? I did notice that the Valiant has this cork-like gasket around the gas filler tube opening, which is compressed, half broken and missing on a few places, which would almost suggest that air could pass it but somehow doesn’t.

After refueling I now check if the gas cap is loose enough that air can pass as turning until it feels tight gets me into trouble.

Is there something I can change so I can safely use the non vented gas caps as offered by people, for both the Barracuda as the Valiant? Should there be a vent somewhere else at the fuel tank (which would surprise me as the filler necks both are inside the car body)? I am quite confused…