When you are talking to a person and see that one of their eyes is looking at you and the other is looking somewhere else.
A.K.A. - Cockeyed
His "Jimmy Eye" drives me crazy. I never know if he is looking at me or someone else when we talk.
As of or pertaining to of one or more eyes on a persons face becoming lazy, especially when drunk.
"Joe was so pants clowned that he was giving the entire romm the jimmy eye."