Didn't know about Amae but I know the feeling. It has a touch of homefulness mixed with the safety felt during a storm (is there a word for it?)
Nakhes though... I have a feeling that the translation or explanation of it is not correct.
There is a word we say in Arabic that sounds exactly the same and many people use in a different context (or the use can be explained otherwise).
Nakhes: Perhaps your youngest has just crawled for the first time, or your oldest has cooked a quiche. Seeing a child achieve something—anything!—can make the heart feel like it’s about to burst with joy. In Yiddish there’s a special word for this feeling: nakhes (pronounced: na-khez, with the kh pronounced like the ch in loch). It makes parents kvell (crow with delight) over even the littlest achievements of their squirming offspring, binding the generations together in a shared feeling of success
Nakhes is the Arabic use is when you are jinxed or cursed. It can be used as a verb. To nakhes someone is to curse them. Said in the example from the article, it would mean more like "keep the curse away", like knocking on wood...
But I have a feeling that this could be one of those words that diverted its meaning from the common ancestral language.
Thinking about it, it could be related to the Hebrew Nekhes, which is like property or wealth. Which makes the explanation given by the article work. I will do some research 😁