I would sleep on the question appropriately?

Question

I just got done reading a book and the last sentence in the book is shown above. Would anyone happen to know the meaning of the sentence? It came from the book The Whistling Season by Ivan Doig.

Answer 1

To me it means that the answer will come after a good night's sleep. Often when you're tired, you can't think straight. And when you put the problem out of your mind during sleep, the answer can sometimes come to you automatically, out of the blue when you're awake and refreshed. Of course not having read the book, I'm not sure what why the word, "appropriately" appears.

Answer 2

The writer is saying he/she will give it much thought.