The head is a very important part of dancing. It influences partnership, balance, power, rotation, movement, just about every aspect of physical movement either solo or in partnership. The head position determines "The Look". "The Look" does not determine your head position.
Head position is not a static position. There is not "A Position" for your head. It is constantly changing and adjusting depending on how you are moving.
When you dance Latin your partnership resembles the letter "A". Your head position is "straight ahead" which causes a slight forward lean in your posture resulting in the "A" look of your partnership. When you dance Smooth your partnership resembles the letter "Y". Your head position is "up" (as if you are looking through the bi-focal portion of your glasses). This causes a backward position of your upper body, thus the "Y".
The Bolero (even though defined as a Latin dance) has a Smooth frame. This is because it is danced close together and has constant rotation. I talk about the head position as having your chin over your left shoulder. This is the general position but it is constantly adjusting and not frozen to your shoulder as if you have a stiff neck.
In rotational partnership movements you want your head on the outside of the circle formed by the frame, but it is not static. It is constantly adjusting in relation to the partnership to maintain the rotation and balance. In rotational solo movements you want your head directly balanced on top of your body.
When dancing solo elements your head position is based on a "Two Legged Animal" and when you dance partnership elements your head position is based on a "Four Legged Animal.
Your head is a living and breathing entity that moves and adjusts to your movements. It must be responsive to your body action. Your head fine tunes your bodies physical movements and is what defines "The Look".