A second responder is the second person who responds to an emergency. The second responder is usually the first responder's bitch.
Dialogue Between a First and Second Responder
Second Responder: I'm here! What happened?
First Responder: Well, it's about time. What took you so long?
Second Responder: You see....
First Responder: Ugh, I don't want to hear it. You might as well be the third responder.
Second Responder: Yikes! That guy's a real a**hole.