How important is eye contact for creating/inducing attraction & showing showing "confidence" towards them?
What is the optimal eye locking duration between 2 persons for inducing this attraction?
It's very important, and a good way to show/build confidence as well. If you've ever looked at two crazy people fighting you can see how intensely they look at each other - they're trying to show off how confident they are and intimidate one another.
Here's the thing though, you want to keep and hold eye contact when it's normal or "feels right," but not do it to an excessive amount to where she would be able to feel like you're conciously trying to control your eye contact in order to seem differently than you feel in your mind - females are very good at picking up sublties like that - however, they are very bad at explaining them usually.
For instance, if you just walked up to them and started talking to them and stared at them like a zombie they wouldn't break down why they didn't like that...or even most of the time know logically why they didn't like that...they would just be able to pick up on the fact that something is off and then label such person as "creepy." That's mostly for the stereotypical blondes tho, lol :) It's like a feeling they'd get or perceive that has been developed over thousands and thousands of years of evolution.
So, the right advice is if it's for a man, would be to hold eye contact a bit moreso than you usually feel like is proper but, don't be a zombie either. Eventually the more you push it, the more you'll realize what the proper timing is for each and every situation.
It's also one of many, many, many "microbehaviors" that women pick up on which can influence whether they like you or not. Like, you could get a girl to like you by not having eye contact with her too. In fact, there are so many of these "microbehaviors" you can't really consciously control all of them (in the ideal scenario they are controlled subconsciously because you genuinely feel that way), but at least try to practice a few of them, if you're asking for yourself.
There is none. It's all about what feels the most natural and pushing yourself farther each time to essentially try everything til you figure out, subconsciously what the right amount of time each where. This process cannot really be done consciously.
If you want to know more about all this and go really, really deep with it, post a comment with @Taal in it and I'll point you towards a website.
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While eye contact is certainly important in social interaction I think you should beware pseudoscientific dating advice based on manufacturing "attraction" between men and women. Since this site is about science, let me point to a couple of areas of empirical research looking at eye contact.
First, there are quite a few experimental papers showing that (pictures of) faces with direct gaze (looking towards you) capture and hold attention, are remembered better, and that they are rated as more attractive. For details see this pdf. There are other similar papers.
Second, there is a long tradition of looking at gaze in non-verbal behaviour. Basically, although this shows that people are sensitive to direct gaze it is only one of many cues related to conversation etc. A classic review is here. Interestingly, the timing of direct gaze (when you look and when you look away) is very important in conversation.
This suggests to me that both looking at someone too long, and not looking at them enough or at awkward times, can cause interactions to suffer. Atypical eye contact is a diagnostic criterion for autism, which is normally associated with difficulties in socialising.