Question: if my private key is, say, 12 BIP39 words and a 13th-word password, is there any way someone who knows or guesses those 12 words will know there is a 13th word password?

i.e. would they know the 12 words are a valid key and they just need to figure out the password, or will they simply have to assume the 12 words were not in fact a valid key?

The 13th word creates an entirely new key, so I’m assuming there’s no way for an attacker to know “they’re on the right track”, right?