Interesting: I heard today, that the [https://en.wikipedia.org/wiki/Duane_syndrome|duane syndrome ](a condition I had since birth) appears mostly in women and mostly in the left eye.

"on attempted abduction, stimulation of the lateral rectus via the oculomotor nerve will be accompanied by stimulation of the opposing medial rectus via the same nerve; a muscle which works to adduct the eye. Thus, co-contraction of the muscles takes place, limiting the amount of movement achievable and also resulting in retraction of the eye into the socket." 
"in most cases the abducens nucleus and nerve are absent or hypoplastic, and the lateral rectus muscle is innervated by a branch of the oculomotor nerve"

That means while the ((Sensory - Eye Muscles|muscles)) aren't affected, the cranial ((Nervous - Motoric Innervation|nerves)) steering their actions are wired so that they prohibit looking to the side (mostly, left eye looking towards left side). 
Paralysis of muscle function and retraction of the eye seem to fit with a parasympathetic freeze-reaction in a UDIN moment. The eye muscles are closely connected to the vagus ((Nervous - System Overview|nerve)) (that's what we use in EMDR or the eye sequence in EFT)

Assuming that the majority of people diagnosed would be right-handed women, a hypothesis might be that before or during pregnancy, the mother and her baby had a conflict of "not being able/allowed to look in the direction of the child or mother", in a shock situation.
I recognize having had such a conflict as a prematurely born twin being separated from mother and sister in the incubator. 
But obviously, the pattern must stem from before my birth, installing nerves with changed function. I could imagine scenes in wartime that may have coined that, yet my twin sister was not affected.

I also had corneal astigmatism diagnosed in early childhood, probably from that same conflict at birth. Losing people out of sight, or longing for to see them in order to stay calm, was a huge stress trigger for me as child. In later youth I developed more autonomy as an answer to being pointed out as different. This led me finally to not wear glasses and to compensate fairly well. Peripheral vision is there even on the left paralysed side of the left eye.