Head Gesture To Tell Someone To Leave
Related notions are:
He waved me away and She nodded me away
Wave-away meaning
(idiomatic) To reject or dismiss with a hand gesture
Your dictionary
Nod = If you nod, you bend your head once, as a way of saying hello or goodbye
Collins Dictionary
Hence nod away is to indicate goodbye and nod in is to invite in.
Google ngram has statistics for nod them away and shows examples such as
Any time someone approached, Ophelia groaned, and Colin nodded them away.
Chasing the Heiress