It is still surprises me how much I do not see the left eye/ face even when I plan to make the connection. I will start talking to someone and find myself talking and relating to the right eye/face of someone else. It often takes a deliberate recognition I am not doing what I think I am doing.
I have had different reactions when I make the left eye to left eye connection. Many are positive, some are negative and I do not know if I am reading something into this that may not be there.
However to jump into the lake of speculation I feel there is a difference in the way I connect and people respond with the left eye. When I am in the left eye mode I seem to get out of my usual rational/worried mode and make a more personal connection. It might be just the difference of making the connection creates a placebo effect within myself, but I do not feel this to be the case. In replaying the way I felt and thought afterwards there seems to be a difference in the way I am mentating. A more immediate sense of the other person with my anxieties on the periphery.
*Further thoughts (jumping into the ocean of speculation)
Going back again to this post and this article how would my brain respond to essentially different signals through the amygdala. How I think I viewed someone's face was always right eye to right eye with my left eye seeing more the periphery on the right side of the other person. I am postulating that my left amygdala remains somewhat inactive/reflexive in my normal communications with others. Seeing and processing the left side while using the left eye to initiate leads to a more refined processing/reaction on my left giving me a different feel of the interaction (and conveying a more relaxed feel to the person I am communicating to.)