I would think he'd be thinking "Ok, she's staring at me...I can't help but hold it because it's awkward...Maybe she'll loook away if I keep staring" Lol jk!
I don't think anything runs through their minds. My mind kind of freezes when a guy looks (stares) into my eyes. Usually they like you or find you attractive. Sometimes it means they wanna kiss you. The eyes are very flirty and can tell someone you like them without saying any words.