When I am jumping to the other hand, sometimes I catch myself splitting the difference between my over the arrow eye and the other. When this happens, I blink the off arrow eye while drawing. I draw with a Hill style spread/ swing draw, I need to get a feel from the beginning of the motion that the arrow is heading to where I want, so the last 6" of draw is like pulling the arrow backwards on its flight line to my anchor.
For me, it is better if I do not mix left to right all the time. While I have always done practice draws both sides to help keep balanced, shooting back and forth during a shooting session gives the brain a lot to do. If I spend a long session getting use to shooting right handed, I hunt right handed for a while. Then when I go back to being a lefty, I do some concentrated target work and then remain a lefty for a while when I hunt.
I am and have always been ambidextrous, I have no dominant eye, but hand eye coordination is still something that I need to groove in.