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1.
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.
by Kenny "Fucking" Powers March 08, 2010
 
2.
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."
by The JZA & The RZA August 26, 2004