I am a right-handed shooter. I do some things left-handed like writing and eating, but the rest of my actions prefer the right hand. So once I identified my eye dominance as a part of my practice, I was not shocked to find I was also left eye dominant. This is called Cross-Eye Dominance, a righty shooter with a lefty eye.
Your eyes are incredibly complex input devices that provide the brain with millions of bits of information each microsecond. They must also work together seamlessly in order to provide your brain a clear and focused, three dimensional sight picture. Without this harmony, your vision would be like looking through just one eye. Very little depth perception and peripheral vision.
But we soon learn that focusing our sight picture requires us to employ focus on both our sights, near to us, and our target, likely much further away. This dissonance confuses our eyes. If you are inexperienced with shooting a pistol with bother eyes open, as is the preferred method for Military and Law Enforcement (see The Pivot Technique), you will quickly learn your brain may not be pleased with your choice. Hence why most shooters unnaturally squint one eye when they aim.
In most cases, one eye dominates over the other. You don't really notice it, but your brain decided a long time ago that it simply prefers one eye. Much of this has to do with how you developed into a left or right-handed person, but suffice to say, you can't really train your brain to pick a dominant eye.
Knowing your eye dominance is critical to become an efficient shooter. A rapid sight picture can be easily obtained if your eyes are told how to do it. Shooting with both eyes open, however makes this especially difficult for a lot of shooters. Many times they see two sight pictures, one that usually appears much more clear than the other. And employing the clearer picture may actually make you miss the target entirely.
DETERMINING YOUR EYE DOMINANCE
Over 2/3rds of the population are right-eye dominant, and dominance does not necessarily follow handedness. In most cases, however, a right-handed shooter is right eye dominant. There are a few ways to determine your own eye dominance, one way without any assistance is called the Miles Test.
Simply outstretch your hands in front of your face, as far as you can, with your palms facing out. Now form a small triangle between your thumbs and index fingers. Then, with both eyes open, gaze through this triangle at a specific point about 20 feet away. Now close your left eye, did the object disappear? If not, you are right-eye dominant. If closing your right eye reveals the object, your dominance is on the left.
Here is a video demonstration of this test.
So in this test, one eye sees the object and the other appears to be looking somewhere else. This is not a malfunction, it it the way our eyes have learned to create a wide field of view, meanwhile allowing us to focus on an object directly in front of us.
If you employ the eyes wide open technique, which is naturally what you will do, involuntarily, in a live fore situation, you need to know which eye is dominant. Which sight picture you will employ to align your aim in order to place shots accurately on your target.
If you struggle with sight picture using eyes wide open, you may want to try pivoting your head to align your dominant eye with your sights (see Pivot Technique).
Whatever you choose, make sure it works for you. The goal is to place shots on target accurately and quickly. However you get there is your own preference.