Dr. Barry Nolt on cross-firing and gun fit
https://www.drbarrynolt.com/shooting-glasses/shooting-articles-by-dr-nolt/why-did-i-miss/

Dr Richard Colo discussing eye dominance and clay target shooting
https://www.youtube.com/watch?v=FD3TKy-FCnA

And the extremely short version is that the dominant eye is not necessarily the eye with the best visual acuity, but the one with the "best" visual processing. This is very likely the issue with women who are much more likely to need some form of off-eye masking but who on formal testing are actually not much more cross-dominant than men.
Visual evoked potentials have shown that dominance is related to the difference in latency (speed of the impulse to the visual cortex) and amplitude (amount of impulse).
http://iosrjournals.org/iosr-jdms/papers/Vol2-issue4/D0241924.pdf

Obviously our wonderful brains CAN switch dominance if one eye is severally compromised.