Learn English – What does “There but for the grace of God — goes God.” mean

Wikipedia mentions the following:

Diogenes Laërtius records the legend that he died by throwing himself into an active volcano (Mount Etna in Sicily), so that people would believe his body had vanished and he had turned into an immortal god; the volcano, however, threw back one of his bronze sandals, revealing the deceit.

Although I cannot say I ever heard the expression used, I would assume, based on this description, that Empedocles’ sandal is the sign that gives away a deceit. I imagine it could be used in a sentence like this:

The credit card bill that he carelessly had left on the table for his wife to find turned out to be his Empedocles’ sandal; it revealed he had spent the weekend in a Paris hotel instead of working overtime at the office.

I suggest the word implicit (implicitly, in the first example in the question):

1. Suggested though not directly expressed: comments seen as implicit criticism of the policies

...

2. (implicit in) Always to be found in; essentially connected with: the values implicit in the school ethos