Sharks it is! This month's Smithsonian has an article on Great Whites, and they've noticed that the shark will look people in the eye: when they're in the water or when they're on a boat. The theory is that eye-seeking behaviour evolved because mammals are a main prey for Great Whites (seals, iirc), and seal eyes are actually a decent source of information for the predator.
It's so distant that I can't help but think that it's a type of convergent evolution.
Eye-seeking behaviour is a fairly ancient pathway, and I believe that it's an essential component of an animal evolving "a Theory of Mind". Many animals are born with the instinct to seek out 'eye contact', which shows how deep it is in our brainstem. One of my pet theories is that autism is connected to a breakdown in the eye-seeking instinct, and thus it hurts the child's ability to form a Theory of Mind on an intuitive level.
Brighteye is up.