I'm left-handed & right eyed.
My solution has been to tip the handgun toward my strong eye & turn my head slightly more to my strong side.
When it comes to handguns, I don't recommend shooting with one eye closed.
In this picture you can see the alignment of my strong eye & how far removed from the sight picture my weak eye is when performed this way.
(yes...the firearm IS LOADED, but there in NO ONE behind the camera. The self timer was used for it & it's an old camera & I wouldn't care if it was destroyed.)