For a lot of us on here, myself certainly included, eye contact among humans is a confusing and often unpleasant thing. I read lots of articles, including this one at a Police Training Site which states, "when two people are conversing about a topic of mutual interest the normal level of eye-to-eye contact is between 30 – 60% of the time. This is referred to as mutual gaze." YIKES!
Though humans are odd and perplexing, I find that dogs make a lot of sense. In the natural world, eye contact is about dominance. Generally, when two animals (or human and dog) make eye contact, the first one to look away is the submissive beast in the pecking order.
One of the simplest ways to establish dominance with a new pet dog is to hold his face firmly in your hands several inches from your face and stare into his eyes. A dominant dog will stare back for a few seconds to over a minute, depending on how strong willed they are. This is phase one. Then they will begin averting their gaze and struggling to get away. This is phase two. Then they will begin licking their tongue out repeatedly, the final sign of submission, while glancing at you for short periods of time.
In this process, you'll notice two distinct "types of look", the "commanding" and the "receiving". In other words there is always somebody telling others what to do and somebody looking to the leader to see what to do. In human terms, these might be called the "hard stare" and "anxious glance" respectively. These are completely natural and normal in the animal kingdom. Dogs aren't threatened or traumatized by being part of a "pecking order". Rather, they are comfortable and at ease when the hierarchy of the pack is clear and they have an established place therein.
The difficulty comes about in this so called "mutual gaze" among humans. I would guess that this odd "third" kind of eye contact is perplexing to most people in the spectrum. Subconsciously, our two main "eye signals", both which we give out and receive are among the first two "natural" forms of eye contact.
Thus we are often perceived as arrogant and domineering (and thus despised) or we are perceived as shy submissive sheep (and thus bullied, bossed around and despised). I'm really not sure exactly how to apply my observations for the benefit of WP folks. Mainly, I just like dogs.