I'm also left eye dominant and right handed. Due to astigmatism, I only use scopes on the rifles, so I simply close my left eye when sighting.
It may not be ideal, of course, but that's the way I've been shooting for 30+ years, I'm kinda set in my little ways by now.
I've been reading on this. There's lots of identical advice that aims to make me use my dominant eye (meaning, learn to shoot left handed, else train the right eye to become dominant). Not one of those advice told me
why it mattered at all to use the dominant eye outside of "fast acquisition" target shooting situations.
I finally found some useful info on a pamphlet from usashooting.org:
Squinting or closing of the non-aiming eye to eliminate the double image of the front sight can cause eye fatigue and muscle strain. Additionally, by closing the non-aiming eye, that pupil will dilate because it is not receiving the amount of light it normally would, and because of a sympathetic response, the aiming eye’s pupil will open more than normal. This can cause a loss of focusing ability and increase eye fatigue. As coaches, we should strive to have our athletes utilize the body’s natural tools in the performance of a task; therefore, both eyes should remain open. The solution for the double image is to use an occluder. Often made of an opaque material like target paper or a translucent material like plastic milk carton, an occluder is an object that blocks some of the field of view reaching the nonshooting eye. Translucent material allows some diffused light to enter the non-shooting eye, allowing both eyes to receive similar amounts of light. Occluders are attached to the either the rear sight or the shooter’s glasses. Avoid black color or covering the eye completely with an eye patch, as this will trigger the sympathetic pupil response.
I may try that patch on the left glasses, see if it does anything for me.
