When we shoot our bows our shoulders are on an angle to the target, but we must keep our heads square onto the target. When a hawk dives on a mouse it does not hold its head sideways but holds its head square on, to focus. Predators have their eyes in the front of the head so the eyes can focus or triangulate on a single spot.
Try this: look at a spot on the wall. Now slowly turn your head to the right. You will see as your head turns right you will start to see the spot become fuzzier and finally you will see double vision and can only clear your vision by closing your left eye. By the time you have turned your head that far right you will notice the bridge of your nose is also getting in the way of your dominant eye causing a shadow on the target.
If your form is such that you hold your hold head far right, shooting with one eye will help. I believe holding your head square with both eyes on the spot is what mother nature intended for a predator and it works best for pin pointing a spot.
A tool I often use to tweak my aim is to squint my weak eye a bit. If I put a book a few inches in front my face, I find my left eye does not see quite as clearly as the right eye. No one has 20/20 vision.
If I think of my shot sequence I'd say I look at the target with both eyes, then I look at the point of aim as I draw with both eyes open, and as I get anchored, I squint the left eye a bit to clear the vision for the final aim.
Try drawing and experimenting a bit. Look at the point of aim and squint your weak eye a bit. Don't squint the dominant eye. By doing this you get the depth perception of two eyes but the clear focus of your dominant eye.
Hold your thumb six inches in front of you. You will see it but your eyes are crossed. The thumb is clear and the background is blurry. If you focus on the arrow tip your eyes cross there or at twenty yards your eyes cross there. Whatever spot we focus on that spot is clear but further or closer parts of our sight picture are blurry.
Another problem with holding the head to the right is "weak eye take-over". If your head is held right your left (or weak) eye is closer to the target than the right dominant eye. At a certain angle the left eye will take over, being closer but you won't know because you only see one thing. Just like your finger jumps back and forth when you close and open your right eye, when the weak eye takes over, you move the arrow left and shoot left.
The first step in archery is to look at the target head square-on with both eyes and then take your stance. In this way your body will naturally line up to the target while holding your head in the best position to aim. Don't take your stance and then look at the target.