P-Dad,
You're not being a pest at all! We love the questions.
Softball Ump has given you a good answer. The ASA umpire manual has specific information to cover the play you describe. The instruction given:
"If a runner misses home plate and the catcher misses the tag, the umpire should hesitate slightly to allow the players to finish the play, either the runner reaching to tag the plate or the catcher reaching to tag the runner. If no tag is made, the umpire should declare the runner SAFE. If a proper appeal is made, then the umpire should call the runner OUT.
There are two reasons why we advocate this procedure. 1) we do NOT want to tip either team that the play may not be over, and; 2) a runner is assumed SAFE until put out. If a proper appeal is NOT made, the runner is safe."
For the umpire to give no signal on this play is not the proper procedure. After the slight hesitation, the safe signal and call should be made. If NSA is teaching something different than ASA (I don't think they do), one of the NSA guys would have to check in a let us know.
The reason this isn't a "leaving the basepath" issue is that the runner walking toward the dugout is not in the act of avoiding a tag attempt by the catcher. The runner can come back and touch the plate anytime before she enters the dugout, or dead ball territory, or before the next pitch.
But there is the potential for this to become a basepath violation, and I have actually seen this happen before.
Suppose we have a sliding runner who just misses the plate and a catcher who misses the tag. The runner gets up and begins walking toward the dugout opening. The coaches yell for her to go back and touch the plate. The catcher is standing near home plate, between the plate and the runner.
If the runner heads back to the plate and the catcher is attempting a tag, now the runner has established a basepath that is a straight line from her position directly to the plate.
If she deviates more than three feet from that newly established basepath, while trying to avoid a tag from the catcher, she would be out for the basepath violation.