I am making an easier connection in seeing people's left eye with my left eye. It is somewhat easier seeing a persona expressed in the left half of someone's face. Trying to put the left tongue in the dominant position seems to play in with the movement of my left eye. The 'tightness' that spreads to the whole left side of the head includes my left eye and as I move my left eye I feel a corresponding pull on the head.. If I switch back to my normal right mode there is no sense of tightness and I turn my head in a way that feels normal to me.
When I switch back and forth between my two modes it feels like I typically hold the right eye in a slight position of advantage with the left eye slightly disadvantaged. To switch to the left eye dominant position it seems to help as ask the right eye to relax backward as the left eye comes forward and centers. (It is easier with right eye closed but does not feel like it needs the right eye closed) The dominance of the eye feels to correspond both to the amount of seeing and the relationship of turning the head.