When a person has a compulsive need to send the last text, regardless of whether or not they add to the conversation or say anything meaningful.
Me: Should we meet at five?
John: Sounds good!
Me: Perfect! See you then
John: Yup!
John: Wanna get food?
Me: Yeah, I'll be downstairs in a few
John: Cool
Me: Cool
John: Cool
Me: Cool
John: Cool
Me: I think you have Last Text Syndrome
John: what?
Me: (gives up, develops alcoholism)