For the hit and run, if there was potential of a play at 2B - (Ie the BR is safe or there is a run down)
BU would never rotate home.
BU would only rotate home with communication to his partner when he is no longer employed.
This same concept applies when he is "out and should stay out" - such as an outside foul line call at 1B.
Well at least cover home. BU doesnt need to spectate or cheerlead the PU, they can be employed at home.
IF BR is safe on the hit and run - BU should never rotate home.
I dont think that would be too difficult to teach to a national level umpire.
Even texas baseball umpires understand it