Me? Naah, if he was staring at me like that, I'll stare back in his eyes so closely, he can tell what I had for lunch. If he turns, I will too, so our eyes can still stare at each other.
IF he was doing that to someone else, I'd 'invite' him to keep doing it, but to do it to me instead, because I like being stared at, and if he wouldn't, I'd get irritated, so he best impress me with his staring skills because he's a nice guy, and neither of us are gonna budge till he proves to me what a nice guy he is, and that what he's doing is perfectly fine.