Eyes are important. You remember all those scenes where the bad guy is questioning a child, trying to find people who have hidden, watching the kid's eyes to see if they flicker off in any direction to indicate the location of the hiding place. You probably also remember that the character Violet's first line in The Incredibles is, "He looked at me." In real life, and in the movies, we're constantly watching people's eyes - characters' eyes - to learn things about what they are thinking and feeling.
Just because you're working in words - writing a story rather than a movie - doesn't mean you should ignore the power of eye gaze. It's one of the most important non-verbal cues that we watch for, and if it's missing, readers will sense a huge gap in your story.
Eye gaze is an excellent tool for reinforcing point of view. To me there's a wonderful contrast between talking about the things seen by the POV character - where I explicitly try to avoid saying "I saw" - and giving descriptions of the way that a non-POV character's eyes move. In this context, having your pov character "look" makes it a conscious gesture of the eyes. Here's an impromptu example:
I turned. Josephine was standing in the doorway. (1) When I looked at her (2), she dropped her gaze away (3).
1. POV character's observation, no mention of "seeing"
2. POV character makes a deliberate eye gesture: placing gaze on Josephine.
3. POV character observes movement of Josephine's eyes, which suggests an emotional state.
We are taught throughout life to manage our eye gaze. "Look at me when I'm talking to you!" "How dare you give me that look?" "As you speak, make sure you're looking out across the crowd and making eye contact with individuals." Because of this, we form expectations about what different eye gaze positions and styles mean, and those expectations can help you in your story. Talking about eye movements or what someone is looking at is a great way to externalize one character's assessment of another character. It's also a great way to "show don't tell."
Different cultures place different value on eye gaze. I had a friend once who was having a period of difficulty with job interviews, and someone else suspected that his style of making eye contact might be at fault. In my local culture, students in school are expected to make eye contact with teachers as a way of indicating that they're paying attention. In other cultures (such as Japanese or Native American), making eye contact with a teacher is considered inappropriate and presumptuous, possibly an affront. If you're working with an alien group or an alternate world, keep this in mind, because it can give you lots of opportunities for creating difference and possible misunderstanding.
Because I like this stuff, I've created a special instance of eye gaze that I'd like to share from my own work. The Imbati servant caste of Varin has a special set of "gaze-gesture codes" that manservants use in order to communicate when speaking is not appropriate (for example, when their masters are speaking and they can't interrupt). It's not a language, and not universal to the caste, since it's taught explicitly to the elite manservant group. However, the most basic gaze gestures are known to most Imbati and can be used in place of speech whenever they would like to use them. Some examples are "permission," "apology," "request," etc.
Recently I've noticed a sort of common gaze language - or more accurately, eye language - emerging from the portrayal of eyes in animated films. Both Pixar and Dreamworks make use of what I call the "shrinking eye." When characters are shocked or frightened, their pupils shrink down to tiny dots. When Toothless the dragon is angry and ready to pounce, his pupils are small; when he's friendly, they're large.
In fact, this is contrary to my observations of nature. I used to play a game with my cat Folly. I'd stare her down and try to get her to pounce at me by using nothing more than my eye gaze. I could always tell when she was about to pounce because her pupils would abruptly expand. Expand - they'd get so big I could scarcely see her irises, and a split second later, she'd jump.
I've asked myself why in the world the shrinking eye would be so effective at conveying fear or shock, and I've come to this conclusion: pupil size is only one indicator of shock. The wideness of the eyes is another major indicator - probably even a more obvious one. When an animated character experiences shrinking eye, not only the pupils but the irises get smaller, leading to a significant expansion in the white of the eye. By using the shrinking eye, the animators are able to convey an extreme widening of the eye without having to have the eyes expand and take over the head (as they, and mouths, do quite often in anime-style animation). In the case of Toothless the Dragon, the pupil not only expanded but distorted, becoming less oval and more square. The result was an optical illusion that made his eyes look more round - more cute - without requiring the animators to change the shape of the eye and create a weird distortion effect on the dragon's face.
I wonder if you've noticed this trend in animated movies, as I have... I hope the commonness of these effects doesn't lead to them becoming the accepted method. Too much uniformity detracts from creativity, in my mind.
Anyway, try spending some time concentrating on how people use their eyes. It could give you some ideas for your latest story.