My earlier post about shooters being made or born started a discussion of eye dominance. Almost everyone has one eye that is stronger than the other, just as they are left-handed or right handed. While many people have their strong eye and strong hand on the same side, not everyone does. The question was raised whether it is better to shoot from your dominant hand or dominant eye side if they are not one and the same.
With new shooters, I strongly believe you should test them for eye dominance and have them shoot from their dominant eye side. Even if someone has been shooting for a few years on the "wrong" side, I think switching is a good idea. Otherwise they will have to shoot with one eye closed.
Now, there are shooters who do very well with one eye closed. The great trapshooter Nora Ross is the best known one-eyed shooter, and her achievements speak for themselves. Check out her one-eyed form at 1:32 of this clip.
Nevertheless, if you can shoot with both eyes open, you should. Shooting one-eyed makes you over-aware of the gun. Two-eyed shooters see the gun as an insubstantial blur; one eyed shooters see the gun in sharp focus. The better you see it, the more likely you are to aim it, and aiming is the worst way to shoot a shotgun. Your eye-to-hand coordination and subconscious mind are much more effective at putting a gun on target than your conscious, aiming mind can ever be.
Some people, like my son John, are center-dominant, which is like being ambidextrous, but instead of two equally strong hands he has two equally strong eyes. For him the answer is blocking out one eye, as seen in the picture. Everyone else should shoot with both eyes open.