A gifted and truly instinctive shooter is something to behold. I admire the devil out of them.
They don't need to rely on their dominant eye working in conjunction with their strong hand. They can shoot from ungodly positions, cant the bow radically, even float their anchor, and still hit with astonshing accuracy. Guys like Bear, Ferguson come to mind. Dan Fitzgerald never ceases to amaze me...
Unfortunately most of us (including me) ain't them. We need to use our dominant eye/ strong hand in coordination and develop consistent repeatable form to shoot effectively.
My son is right handed/left eye dominant, which we discovered when he was 5 years old. To watch him contort himself to get his left eye across the string or a firearm stock was painful.
We simply switched him to LH for anything required aiming (rifle, shotgun, bow). Took him about a month to get comfortable, and he hasn't had a problem since. He's going to be 28 this year, a career regular Army soldier, and a crack shot.
I'm left handed/left eye dominant. Back when I first picked up a bow in the early 60's, I had no instruction and the uncle that gave me the bow knew nothing about archery. Needless to say, it was right handed.
I didn't even know LH bows were made until I was 13, when I got a copy of the 1968 edition of Fred Bear's Archer's Bible. There on the cover was a picture of Fred shooting a left handed bow! I had been having hell's own time shooting various right hand bows left handed for years, and all of a sudden I knew why.
I then got my first left handed bow (a Shakespeare Sierra 45#), and it was like a miracle. All of a sudden, the arrow was going where I was looking. Unreal!
You get your dominant eye and strong hand working together, and you won't believe the difference...