A third responder is the third person who responds to an emergency. The third responder is the worst.
Dialogue Between a First, Second, and Third Responder
First Responder: Well, it's about f**king time you got here."
Third Responder: Whatever...
Second Responder: In all the years we've been dealing with emergencies, you're never the first or second to respond!
First Responder: Yeah, what's that about?
Third Responder: Geez, you guys are such gunners... I'm gonna go grab something to eat.