Oh, I found this:
Reading the Eyes in Body Language
It suggests attraction. But I am also thinking it is more then that. Not just attraction, but severe interest in completely grasping what the other person is trying to convey.
It is quite interesting though - and I do wonder what it looks like, because to him, it is like a falcon - but in a more gentle way, he also indicated it is quite disconcerting, and difficult for him to follow. I have also noticed other people pulling their head back from my gaze at times. I can be rather intense mentally.
Please share with all of us your own eye contact habits, whether it is avoidance, or staring, or back and forth or whatever. Let us see if our personality disorder has any pattern in this way.