You can’t teach what you don’t know. And as native speakers, we don’t have to “know” much about our L1 to be able to use it, do we?
I learned about intonation by studying whatever I could find. As with pronunciation (see other post), I read and read, I studied many public speakers, and eventually I was able to synthesize my own ideas about teaching tone. These sources gave me lots to think about, and I learned a great deal from reading them.