This posting is arguably a continuation of this posting.
Here is a theory I am working my way through, slowly. What I'm interested in here is how, specifically, we view portraits in which the subject is looking at the camera, versus portraits in which they are not.
When the subject of a portrait is looking directly at the camera, the viewer reads this as eye contact. We become, at a monkey-brain level, interested in what the subject is thinking. We imagine their mental state. This is the basis of social interaction, and incidentally we're extremely good at this.
When the subject is looking elsewhere, the viewer reads this as unawareness. We are now observing the subject remotely, we are "spying" a little. This is still about social interaction, but we're less interested in what they're thinking. We're evaluating posture, body language, objects and activities. In simple monkey-brain terms, we're probably making a friend-or-foe evaluation.
Anyways, the upshot of this is that we're more likely to read "mood" and "personality" exclusively when we're looking at an eyes-on-the-camera portrait. We're going to project onto the image some idea of the model's mental state, and we're going to be put off if we can't.
We're more likely to read "story" and "history" when the model is looking away from the camera, especially if there are more cues visible: clothing, actions, body language.
I think this means, among other things, that if your model is not looking at the camera, you need to give the frame more room to breathe, give more space around the model's face. This might be the source of the rule of composition which asserts that you should give space in the direction the model is looking, and is, I think, certainly connected to that rule.
The flip side is that when you're doing an environmental portrait, where the props are surround are important, having the model look aside is often the stronger choice, or at any rate the choice the image simpler to look at.