one or both

shoot with both eyes open.

The reason for this is if you close one eye the face muscles are never in the same place twice so this hinders the right eye and means your not consistent each time you take aim.

If you close your left eye with different muscle tension you'll note your right eye line changes.

I have never heard this explained this way before
 
If you have two good eyes it is always best to use both of them for both peripheral and depth of field vision. However, it is almost impossible to shoot a scope with both eyes open when the scope is not in front of the dominate eye. I shoot a scope right handed but since I am left eye dominate I place a small piece of scotch tape on the left lens of my glasses in just the right spot to block the point of aim. This allows the brain to push the dominance to the right eye since the left eye can't see the target clearly. I agree, closing one eye and sighting with a scope never feels the same time after time and both eyes open is definitely more relaxed.