The usually-unconscious act of turning the object of one's romantic desires into a representation of some sort of ideal - a metaphorical "green light" shining across a bay. Often taken to the point where even if one were to successfully court that person, it would be unsatisfying as they would be humanly incapable of living up to the dreamlike figure they'd been built into.
A: Why won't Jay just talk to her if he likes her so much?
B: He's been totally green-lighting her. Even if he manages it, she's not the person he wants to think she is.