I have heard more instructors encourage people to be ambidextrous with their gun usage then to use a non preferred eye.
And even so I think most instructors believe there are more important things to work on then to bring your non-dominant
hand to the same level as your dominant one (I believe both TLG and Tom Givens are not big advocates of non-dominant
hand training as there are other things to work on for bigger gains) .
Working on your non-dominant eye sounds difficult and less useful.
It is also true that these sort of discussions have no clear answer. The last time this came up Mr, White
pointed out that there are GM using every combination of dominant/non-dominant eye/hand and the supposed benefits
and drawbacks are hard to tell. Personally I am absolutely fascinated that someone would choose to train with with
non-dominant eye and non-dominant hand! Why would you think that is a good idea?
Bill Rogers is quite adamant that you must use your dominant eye and which ever hand is on that side even if
it is your non dominant one. After several years of this approach (and encouragement from Tom Givens et al)
I am switching my shooting to my dominant hand. I have not had any instructor encourage the use of the non-dominant eye.
https://pistol-forum.com/showthread....ll=1#post19102