When I switch to left side control of my head it is more like I am discovering the coordination of the different elements than directing them. I can ask for a certain movement such as the turning of my head but there is no way I could have thought of all the separate pieces. However once performing the movement and feeling the different elements of control initiated on the left I can remember them for the next time and try to include them in the movement. The movement feels to be more complete as I discover the different structures that can contribute.
In looking at a person's image in profile that I only see the left side of the head I do see a persona unlike when I view the left side from a full frontal position. What I think I am doing normally in the left profile instance is my right eye dominates and almost makes an assumption what the other person right eye/face/persona is on the clues suggested by the left side image. The dominance of my right eye takes over in reading the left side of the profile. If I put my attention in my left eye I have the same incomplete sense of the persona as I do when see the frontal image. I have to pay attention and scan a few seconds longer before I am able to see a persona suggested. Most of the time the persona is more complete when my right eye is directing the scan than my left.
If I close my right eye and look at a someone in the frontal image I don't have any trouble in ascertaining the persona with the natural inclination of seeing the right eye /face even though I am using only my left eye. However there feels to be a suggestion in myself that my left eye does not come up with the persona but is communicated in my head and my right(left hemisphere) comes up with the image of the persona.
Of course there is a strong possibility that I am completely out to lunch.