amar,
I've become left eye dominant over time...and I shoot fine with both eyes open. Instinctively.
Our eyes are in front of our head. Gives us binocular vision. Like other predators. Gives us depth perception.
Jay Kidwell, in his book on Instinctive Archery, does a very fine graphic that shows if you're gun barreling or gap shooting down the shaft, then you would tend to have the bow more upright, and anchor so the arrow is as close under your DOMINANT eye as possible.
If you shoot with a canted bow, and try to do what most of us call "instinctive" then the vision you would be using is binocular. And that by definition suggests "both eyes open."
No hard fast rules, but then, I would respectfully disagre that eye dominance, is quite the cut'n dried issue as you type it either.
I can't begin to shoot anything with a sight without closing my dominant left eye being a right handed shooter, but this whole "burn a hole and release" idea of instinctive has worked very well for me...occassionally out to 40 yards when my form is solid... so I find eye dominance is NOT a factor in true instinctive shooting..
Again, Jay Kidwell's book really shows some great pictoral representation of both ways of shooting for good insights. He also covers some "hybrid" ways some of us shoot where dominance might raise an issue.