I'm right-handed but shoot left-handed because I am left-eye dominant. And I think initially I might have had a problem siting the front site and the target with both eyes. But I got over it and learned to concentrate on the front site, with the target's red bullseye behind it, using both eyes.
And I just thought this up. If you find yourself closing one eye to site with a handgun, will you do it with a bolt, nail or match as well?
1) take a small but long bolt, nail or match and hold it between the hands
2) simulate holding a handgun and have only the tip of the bolt/nail/match showing
3) site down the hands to stare at the tip
Can you do so with both eyes open or are you closing the weak eye even in this minor exercise?
If you can see the tip of the bolt/nail/match with both eyes open, then seeing the front site/tritium or phosphorescent dot against the target is probably a matter of convincing yourself you can do so with both eyes open. And how do we get good with guns? Right, lots of practice with front siting and keeping both eyes open, sometimes without even firing a round.
"Let those find fault whose wit's so very small,
They've need to show that they can think at all;
Errors, like straws, upon the surface flow;
He who would search for pearls, must dive below." -- John Dryden