The look a person gets on their face while staring at someone intently, sometimes because they think they might recognize them but aren't sure who it is.
If the two parties do not know each other, gawker face can be mistaken for creeper face
Chelsea had some serious gawker face when she thought she saw Josh while driving through town.
You are on a bus and someone wearing headphones or who looks like they think they're watching a TV program gawks in your face. You don't bother to say "Hello!" (or "WTF?!") because you already know they won't answer nor even blink, but instead you heartily remind yourself under your breathe, "(It's just) a brain-dead gawker (oh yeah!)"