Unless the referee holds the ball over his head (S14), then by rule, he hasn't declared it final! (11-1)
And the next D1 referee I see hold the ball over his head following the last play of the game might well be the first.
My point is that while your formal "jurisdiction" ends when the score is declared final, from a practical standpoint, you're "on duty" until you are off the field. Let some player or coach accost you while you are running off the field and see if you still jurisdiction.
NCAA Baseball formalized this position in the last rule change:
Umpire jurisdiction in regard to personal confrontations and unsportsmanlike
conduct directed toward them begins when the umpires enter the game site
and ends when the umpires have left the game site.
A) This ain't baseball.
B) Unless he couldn't get a ball expediently, every FBS R I've ever seen - and I've seen a lot - has held the ball overhead at the end of the game. Maybe you've never seen it, but don't assume your experience matches everyone else on the planet.
C) If somebody acosts us as we are getting off the field, that's somebody else's jurisdiction. We can not impose any penalty. If we can't impose any penalty, then we have no jurisdiction. We report the incident to the proper authority, be it an institutional administrator, a league/conference executive, or a criminal justice authority, and they deal with it.
D) Failure or inability to use Signal 14 doesn't mean the score has not been declared final. I have seen numerous games where the R could not get a ball expediently after the last dead ball, and he just left the field. Are you telling me all those scores are not final? Bovine scatology. We damned sure ain't waitin' around for the kids to kiss and make up.
E) If you do hang around, what are you gonna do? You can't penalize anybody. Are you gonna try to break up a fight? Pretty stupid, on several levels. If you don't get hurt, you run a huge risk of doing something for which you will lose in a law suit. When the day comes that we can fine or suspend somebody for post-game actions, then OK, I'll do my duty, stick around until the players have left the field, and then go. But that day ain't here, and we damned sure ain't gettin' paid for that.