Another vote for dominate eye...Lefty being an alien and an exception to the rule it is near impossible to shoot opposite of your dominate eye and have proper form with both eyes open...
It is possible like mentioned with dominate eye closed and shooting opposite or wearing a pirate patch..which I have seen several do...
In most cases where one can shoot oppiste the shooter is most likely border line with not only left or right hand but also close with left or right eye...
Some of us just couldnt do it...I know I couldnt/cant shoot left handed...
If one for right eye dominat uses the dominate eye test using the right arm straight out with pointy finger on the X of a target...both eyes open...
Close right dominate eye...I... pointing at X close left eye...am now aiming TWO feet plus just at
ten yards to the right of target...
One can visual see the handicap of this very clear...from a aiming standpoint with an open sight shotgun I would miss a moose size critter at ten yards...
Doing so with a rifle utilizing a scope this isnt an issue...even with both eyes open as the scope will take presidence to eye being used...
So with all the above in mind...if one was to shoot with their dominate hand and oppisite dominate eye ..an peep will be absolute nessecary...if peep is magnified ...even better!!!
As a lot of factors can play here...even low light...I suggest trying same hand as strong dominat eye to start!!
JMHO
Neil