Guidance please
 

What is the NFHS rule with regard to a dropped third strike & how far/long does the batter have until they can still try to run to first - i.e. at what point if he has not made an attempt to run to first AND has not been tagged by the catcher do they give of their chance to run?

Casebook 8.1.1 sit B: Summarized If Batter-runner fails to attempt to go to first before the time of the next pitch, he reaches the bench or dugout area or a half inning has ended because the infielders have left the diamond, he is out.

Other codes have it as leaving the dirt circle by home plate.