From what I understand about Thai law, defamation involves a third party. If person A says says to person B something derogatory about person C, person A has defamed person C, right?

But what if you insult someone in private, just between the two of you? That can't be defamation because no third party is involved, right? Like, I tell you you're ugly, but no one else hears. That can't be defamation, but does some other law apply?

Only the law of Natural Selection. Insult then duck.