If you have seen The Karate Kid movie, you will undoubtedly remember the wise old karate master, Mr. Miyagi, telling his student Daniel-san to; “Look eye! Always look eye”.
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Well, not necessarily. At least not in the martial arts.
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In fact, in Japanese culture, excessive eye contact is considered rude. And being rude to people, regardless of culture, is probably not the smartest thing to do if you are trying to avoid getting into a fight.
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When you are faced with violence, your body goes into freeze, flight, or fight mode. Adrenaline is dumped into your bloodstream to give you extra energy to survive the situation.
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But that adrenaline dump can cause several other different effects on your body systems. Such as; Pupil dilation, tunnel vision, and also a loss of depth perception and near vision.
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Humans have two basic visual fields, our ‘foveal focus field’ where we see detail, and our ‘peripheral vision field’ where we detect movement.
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Our foveal focus field is very small, whereas our peripheral vision field is much larger. The foveal field is used primarily for fine motor skills, like reading, threading a needle, etc, and is considered to be slower when reacting to a ‘startle’ response, as opposed to our peripheral field, where reaction time is much faster. Additionally it allows us to notice more of what is going on around us.
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So where exactly should you focus your eye contact in a violent combative encounter? What do I look for?
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You pay attention to movement, as you look for openings! Yes. YOU ARE LOOKING FOR OPENINGS! The openings are where you want to go; to an angle, moving away from what you don’t know, moving towards what you do. You are simply paying attention. You are not looking for any specific movement, not waiting for a punch, kick or grab, you are trying to be alert and aware of anything your attacker does. Paying attention to their movements so that you can react to them, or take advantage of them.
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In effect, reacting to your opponent’s movement WITHOUT looking for that movement. Don’t waste your vision looking for an opponent’s attack. FEEL their attack; HEAR their attack. Use your bodies built in physical startle response mechanism and your peripheral vision, to ‘see’ those openings, which is much more effective than looking into their eyes, waiting for punches or kicks.
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In my humble opinion, looking into your opponent’s eyes, or at the shoulders, or the chest, or the foot… it’s all nonsense. Just look forward, look for openings anywhere you see them, look for opportunities.
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Learn to perceive rather than just see. 
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“Focus too much on the leaf and you miss the tree, Focus too much on the tree and you miss the forest.” – Takuan Soho, Zen Buddhist (1573-1645)
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