Watching the talking heads on the tube and shifting back and forth between the left and right half of people I am viewing, I get much more information from the right side of their heads than the left. My habitual is to see the right side as the side that is talking to me. My right eye crosses my midline easily to make the connection with their right eye. When I make the conscious shift to put my attention in my left eye and cross my midline and shift it to their left eye my tendency is to check back to their right eye to gain more clues.
Putting my attention in my left eye and letting it cross my midline feels to give an immediate subtle difference in the musculature engaged in head posture. I am trying consciously to accentuate that feel. On occasion it feels like I am switching from right side musculature dominated mode to a left side dominated use of my head.