That sounds like an overload sensation. I feel two things - that they want to look inside my soul and the overwhelming feeling that I have no clue what their look means.
I can do it to get on, but here's what I've found out happens (sometimes it's good to be a manager because after your employees know you long enough they tell you these things). I do it and I'm think I'm doing it right for years. I am talking years! Then, suddenly I will say something to one of my employees and they will look at me strangely and say, "You NEVER do it right. Everyone just gets weirded out by it and finally gets over it because we all know you're stranger than s__t and we still like you." I get that about many things. Like I will think I am acutally getting subcontexts and jokes and references to pop culture things, then I say something because I'm comfortable with that person and get told that everyone knows I do it wrong, they just have gotten over it and moved on. That's about the point where I feel like I've put this massive, exhausting effort into it and it didn't work anyway. In the end, they just decided what I knew and how I treated them (fairly, stood up for them, got them decent raises) is what actually made the difference and not my pretense at eye contact and the rest of it.
This sums it up perfectly. I got this in a Christmas card from a uber NT woman (she's a trainer and very feely so we are polar opposites in personality not to mention NT/AS). "You're still strange, but I like ya anyway. Let's do lunch." That is the perfect summation of my forays into the NT world. They end up kind of comical, but for the fact that they exhaust me. (Dealing with me probably exhausts her too.) That woman by the way absolutely hated me when I first worked with her. We've even talked about that. I didn't put it in AS terms because that was 1996 when we met. But, it was a classic NT/AS communication breakdwon. It took three years for her to get comfortable and figure out that I wasn't being mean to her, that I really didn't get it. She honestly did think I was messing with her. She says it was because I was so intelligent (hey, as long as she's impressed!) she just couldn't comprehend that I really couldn't understand those things, but later, she did finally see that it was consistent and happened with everyone, not just her. Now, we do go to lunch or even to some clothing stores! I even took a trip to Colorado with her twice. But, we've also learned how to get along. We don't change who we are, but we just know our limits with each other. We can only handle so much of each other because we are polar opposites. But, that's ok. I'm still strange, but she likes me anyway. She's still overly needy and gushy, but I kind of like her too. 