There was a recent bbc article on some study that basically confirmed that the first person to break eye contact is submitting dominance to the other. Application in attraction would effectively be that the person that breaks eye contact first sees the other person as higher status/value than themselves.

The study did make a very important point that not all acts of eye contact are dominance tests though, in the majority of instances the very first instance of eye contact almost always was.

I think there may be a little more depth to it than this though, a lack of a break in eye contact can be aggressive or creepy. Just because someone manages to hold eye contact longer than the other party doesn't mean that the other person happily accepts this position. In fact such a thing can make someone instantly feel like they dislike the other and become vocally hostile. I personally believe that if someone doesn't have instant attraction to you then the latter is what occurs, holding of eye contact while adding a friendly smile is capable of changing this though, in cases where a reciprocal smile doesn't occur I think immediately talking to them and ensuring a the right message came across is important.

An interesting thing to think about at least, I don't really think anyone should think too much about this and certainly shouldn't allow themselves to get into their heads. Overthinking it just creates unnatural behaviour and unnatural behaviour regularly sends the wrong messages. We all do these things because they're an internal part of the way we all communicate. I think that forcing this behaviour isn't all that important though. If you believe yourself to be above the other person then you'll exhibit these things naturally, instead of trying to force unnatural behaviour try working on the underlying mind and improving that, it should automatically cause you to send the correct corresponding messages automatically.

Hmm.. This is quite messy, I'm not sure whether to equate this with body language or not. I would usually say that assuming body language is good due to research that shows mental pathways work both ways - if we're unhappy we might show unhappy body language but at the same time if we force happy body language it causes happy sections of the brain to start activating and causes a mindset change. I however think this is slightly different as it's more of a silent and unconscious form of communication with another person.

I remember when I was young an old man said to me always make eye contact wen u shake someones hand they'll give you more respect. I did start getting more respect from peeps after that.