Which is it?
It is both. The sign is administered outwardly and it also represents an inward reality. To repeat, the fact that non-paedos have no such sign is indicative that they practically affirm no salvation for infants. This was slightly bearable when their practice was under the nurture of her free-will mother, Anabaptism, because that system denied original sin. But when this practice is taken up under the teaching of original depravity and sola gratia, it is intolerable cruelty.
Watson's book, by the way, is one example of breaking the ninth commandment after another.