Hmm… That didn’t seem right to me, so I looked it up

The “knock, knock, ginger” is linked to a 1967 Childhood in Poetry book by John Mackay Shaw. Behold these glorious verses:

Ginger, Ginger broke a winder, Hit the winda—crack! The baker came out to give ‘im a clout, And landed on his back.

However, we’ve also seen the game called knock down ginger.

This may actually be more accurate, as “knock down” is a term dating to the late 18th century. It refers to knocking on a door by pulling the door knock striker.

Plus, ginger was a common term then as it meant to “ginger up” (move smartly). So, knock the door, leg it in timely fashion.

https://professionalmoron.com/2022/04/18/history-of-knock-knock-ginger/

That feels a bit more like it to me, though surprised it’s not even a century old, I figured it was Victorian