A couple of things here. First, even though the runner from third misses the plate, other runners must be given the opportunity to complete their base running duties. A home run is a dead ball so the appeal is verbal. And can be done by any member of the defense so long as all runners have an opportunity to complete baserunning duties and before they leave the field.Runners on 1st and 3rd with 2 outs.
Batter hits a HR. Runner from 3rd misses home plate. Runner from 1st touches home plate. Batter touches home plate. After both score, the original runner from 3rd is told to go back and touch home.
Is the runner automatically out? Does the defense have to appeal? How many runs score? No harm, no foul?
Because the runner who missed the base was the first one in the series, and constitutes the third out, no following runners can legally score. They can also not return to retouch after proceeding runners have touched. Therefore, no runs score.
see rule 3 section 2 penalty and article 6.