For emotion related info it may have to do with orienting oneself toward affective states by looking at 'close objects' (the body), which would move the eyes downward. For cognitive information maybe it is because the body is out of sight that cognitive information doesn't inadvertently dip into affective states; or that the eyes moving upward orients oneself to 'distance objects', which you could theoretically argue is more attributed to conceptualization. 

A commonality between the two cases.

eyes move upward/downward > less visual objects and less possible interaction with other individuals > less interference with the retrieval (Glenberg, 1997)

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The difference between the two cases

eyes move downward for emotion related info > to be at rest  > more focus on interoceptive sensations

A fascinating finding. Does it only apply to face-to-face interactions? If so, it might be that these eye movements have a signaling function. Analoguous to what Joshua had mentioned, it could mean something like "I am searching the answer in my brain" vs. "in my heart/body" etc.

Not scientific propositions:

- upward to concentrate on the brain, the source of all cognitions;

- downward to concentrate on the hearth and stomach, the engine of all emotions.

Dear colleagues, thank you for many prompt responses. However my query looks for a more scientific answers in terms of connexions with which part of the brain if any. In synergology (body language analysis) we consider acknowledge the gaze aversion according to cognitive related info. It seems that brings the eye movement upward. I am trying to avoid concluding the downward movement relating to emotion just be deduction in opposition to the cognitive level.

Do they? Body language analysis and NLP are notoriously unscientific, and there are numerous myths that are widely repeated with no foundation, such as diagnostic eye movements during lying: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0040259

Gaze aversion is related to cognitively demanding activity though.

I agree with Edward in that the first step before asking "why" would be to find evidence that these kinds of eye movements are really an established phenomenon. I know they are used in NLP and in trauma therapy.  I found some evidence in self-observation, however I don't know of any research corroborating their existence.

Interesting topic though! I hope to hear more!

In order to make sure that we are on the same page, allow to respectfully establish some basic point: 1)I don't pretend that NLP or body language is scientific. However, work by M. Vrij about lie detection became acknowledge by the scientific community around 1998. So, may be there is an opportunity for body language and, especially synergology, to access such recognition in a near future. 2) I absolutely share the position that no such technic allows us to detect lies. In fact, the only way to confirm whether it is a lie is to have a confirmation from the "liar" himself of clear contradicting facts. Finally, I do realize the amount of work and research required to establish a link between the direction of the gaze aversion, the nature of the related info (visual, cognitive, emotion, etc.) and the triggering mechanism that may be located in the brain. So thank you for continuing raising comments and questions on this topics as I make the eye movement my developing expertise.

I pursuit of our scientific approach I appeal to all to see whether someone would be interested doing research on body language. There is a scientific threshold to overpass in order to maximize recognition not only in the activity sectors who use it already but also in the scientific community in general. Interesting topic may be develop from this.

Following.

This information is beautiful