Sam Harris examines it:
One behavior that you can readily notice in many gurus, as well as in their students, is an unusual commitment to maintaining eye contact. In the best case, this behavior emerges from a genuine comfort in the presence of other people and deep interest in their well-being. Given this frame of mind, there may not be a reason to look elsewhere. But maintaining eye contact can also become a way of "acting spiritual"—and an intrusive affectation. Needless to say, there are people who maintain rigid eye lock, not from an attitude of openness and interest—or from a desire to appear open and interested—but as an aggressive and narcissistic show of dominance. (Psychopaths tend to make exceptionally good eye contact.) Whatever the motive behind it, there can be tremendous power in an unwavering gaze.
The Dish 