Yes, semi-automation is achievable. However, obtaining an accurate chin position might be difficult. I have tried recording the Camera Raw filter as an action, but unfortunately, the recording still applies to the previous image.
One can assess the »Select People«-selections via Script now.

// 2025, use it at your own risk;
if (app.documents.length > 0) {
var desc232 = new ActionDescriptor();
desc232.putBoolean( stringIDToTypeID( "selectAllPeople" ), false );
var list4 = new ActionList();
list4.putInteger( 1 );
desc232.putList( stringIDToTypeID( "people" ), list4 );
var list5 = new ActionList();
list5.putString( "Facial skin" );
desc232.putList( stringIDToTypeID( "tagsV2" ), list5 );
var list6 = new ActionList();
list6.putInteger( 10 );
desc232.putList( stringIDToTypeID( "tagsIndices" ), list6 );
executeAction( stringIDToTypeID( "selectPeopleV2" ), desc232, DialogModes.NO );
// check for selection;
if (hasSelection() == true) {
var originalRulerUnits = app.preferences.rulerUnits;
app.preferences.rulerUnits = Units.PIXELS;
alert ("chin "+activeDocument.selection.bounds[3]);
activeDocument.selection.deselect();
app.preferences.rulerUnits = originalRulerUnits;
}
};