If two people make eye contact and someone points at something (without speaking) with only their eyes, what is that called?
Usually we say that the person who is "pointing" with his/her eyes is signaling in that direction (with his/her eyes). For example, "He signaled with his eyes that there were guards standing in the corner".
Other phrases that you could use are, for example:
1. He indicated that ...
2. He gazed to the left to show that ...
Feel free to use any other synonyms that are similar to "signal" or "indicate".
You might also dart a glance at someone or something, meaning that you would look at the subject for a very short time (Macmillan).
Is eye-pointing a complete fallacy? I don't believe it exists as a verb only but don't see why it shouldn't :)
Actually, I've just done a search and found this text:
Eye-pointing is described as "The context-relevant, controlled and intentional use of gaze in order to direct one or more partner's visual attention to any item or object for a deliberate communicative purpose. — About the Eye Pointing Classification Scale - UCL
While you would need a verb (shot, threw, gave, etc.) to supplement this, the glance itself is called a pointed glance:
She shot a pointed glance diagonally toward the kitchen, loath to speak and wake Faith. ... He must have caught the meaning in her glance, because his expression lightened. — Bearly a Chance
Simply glancing at something can be ambiguous. For example, if you're "darting a glance at" the clock, that signals that you're impatient and fails to have any connotation that you're trying to tell someone else to look at the clock too.
Note that giving someone a pointed glance usually means that you're trying to communicate something to them with your expression (not something about them per se).