Eyeballing (infinitive verb) refers to an erotic act of one person licking another person's eyeball. This act does not derive its erotic nature from any actual connection to a sexual organ or classically sexual act. It is only sexually arousing to people with a fetish for tongues, eyeballs, licking, or any combination of them. It was first discovered in Japan, where pornography laws arguably force creative forms of "erotic art" by not easily allowing the depiction of sexual organs.
Guy #1: Dude, you have to come see this website!
Guy #2: Why is that Japanese girl licking the other girl's eye?
Guy #1: That's called eyeballing, it's the latest thing. It gets people off.