1. Impertinent or disrespectful.
b. Impertinent in an entertaining way; impossible to repress or control.
3. Etymology: "resembling sauce", later "impertinent, cheeky" (1530),; from sauce.

The connecting notion is the figurative sense of "piquancy in words or actions." From Old French sauce, sausse, from the noun use of Latin salsa, salsus, "salted"; from Old Latin sallere. "to salt" which came from sal, salis, "salt".

Sauce malapert, "impertinence" (1529), and the slang phrase to have eaten sauce or to "be abusive" (1526).