No, I don't have a problem with obsessively staring at people; my problem is the opposite - people staring at me in odd, rude, and excessive ways.
I may glance at people, look away, and then glance at them again if there is some compelling reason to do so; but mostly, I try to avoid getting caught looking at someone. The last thing I want is some awkward staredown.
I think I have encountered some people who have a similar tendency as you do to stare at people, though. My cousin may be one of these people. Years ago, during a family occasion, I was quite irritated by this cousin staring at me in an excessive manner. I could be in a group, talking to (more or less) other people in this group - but he seemingly didn't stare at these other people...I would be the one whom he would be "locked in" on. I was already feeling quite uncomfortable - with his staring, I felt like an outright freak-show. I was angry that - out of all of the people who were there - I was the one whom he was targeting in this manner.
A few years later, I called him on his behavior - and he claimed to have no memory of it. He simply didn't realize that he was staring at me; apparently, it was some "reflex" that he wasn't fully conscious of. Later on, he sort-of confessed to some "staring problem"; he mentioned that he was taking a class at a community college, and he was staring at the various people in that class. He said that at least a few of the people may have been freaked out by his staring; he didn't mean to offend these people, but he somehow just gets "sucked" into staring at people without realizing it.