The Eyes Have It
"Look into my eyes." In hypnosis or meditation, the first step is often to find a specific spot on which to focus attention. This could be anything, but (apart from a pocket watch) popular culture has focused on the eyes.
It is not the only time that near-mystical powers have been attributed to eye contact. It's supposed link to honesty has been debunked (liars learn quickly that maintaining eye contact is a necessary professional skill) but lives on in our collective minds.
Another study suggested that prolonged eye contact could lead to love. After asking each other 36 questions designed to be progressively more probing and intimate, “Two minutes is just enough to be terrified... Four really goes somewhere.” Personally I think anyone who is interested enough to endure 36 intimate questions followed by a four-minute staredown is, shall we say, pre-disposed to liking you. I would like to see another study with "your place or mine?" as the single control question.
That said, people do find a sense of connection through eye contact, and it is important to get it right. Too little and you seem disengaged. Too much, and you start to look like a creep. According to one study, the correct amount is about 3.2 seconds. Consistent with my view above, they found that a longer time was ok if you feel comfortable, but that generally long periods of sustained contact were viewed as threatening.
An interesting part of the study was a finding that people were more likely to change political opinions in the absence of eye contact. This perhaps allows us not to feel threatened by a view that contrasts with our existing one, and may be a way to avoid confirmation bias (look away when you are hearing a different perspective.)
So, for those looking to persuade, learn to avert your gaze. Unless you are trying to persuade someone to fall in love with you, in which case hold it for four minutes (assuming they do not flee during that time.)