Right-handed and right-eye-dominant. I keep both eyes open for shooting.
I shoot pistols both LH and RH but rifle is too awkward, so only RH for that.
When I did a lot of photography, I focused using my left eye on the viewfinder.
I practice both sides as much as possible in all sports that allow it. Works great for kayaking in all strokes and rolling. Whatever rolling side I practiced more became dominant unless I did both sides in roughly equal amounts. Pseudo-ambidexterity can be learned and improved, but if you stop practicing for a while, your inherently dominant side reasserts itself. But even “pseudo” is very helpful when using hand tools in awkward positions, or when one side is injured.
Unfortunately, my right eye’s astigmatism and cataract are worse than the left eye’s.
BTW, practicing both sides helps for figuring out things that seem weird. For example, I noticed with both PB and air pistol that RH shots often tended to hit left of aim point, and LH shots often tended to hit right of aim point. The wind was not reversing that many times! It had to be either my overall body stance or natural tendencies in hold. (The difference was not there, or was less, when shooting off a front rest.)