Three seconds is entirely too long, even if you’re headed directly at the person. It’s strange when the American “don’t stare” rule combines with the “acknowledge people facing you” rule. We have a long hallway here at work and when you see someone approaching the opposite direction, you have to look at something else until you’re about 1 second from crossing. Then say “Hello” with direct eye contact.
No earlier, no later, or it’ll be weird. Looking natural the whole time is an art-form.
Direct eye contact is part of a communication process. The lack of additional information presents an uncomfortable situation. Direct eye contact for more than a second or two, without any additional form of communication is like calling someone on the phone and then saying nothing when they answer. I think that at the youngest ages some of the reactions are imitations of older children. For young men entering puberty the reaction may be more confrontational because of increasing testosterone levels, but young women may feel just as uncomfortable, or more so, and just aren’t reacting in the same way.
I just happened to glance over at the next driver while at a red light the other day. The guy immediately made a face and glared hard at me for the duration of the light. I just ignored him, which probably made him madder.