Aside from the standard qualities — open-mindedness, clear analytical thinking and communication, patience, experience — I would add teaching how to sound things out on one’s own. If the student only ever uses sheet music to play, the teacher is failing them.
ANY music teacher should give more than occasional assignments to listen to a favorite piece of music, figure out the melody — and if this involves whatever top-40 stuff is on the radio at the time, then the teacher should grit their goddamned teeth and deal — and come back with it written down on a piece of staff paper.
For piano students, the student should then be sent home and told to figure out a left hand. Single-note instrument students should be told to come back next week with some ornaments or embellishments figured out.
These assignments should be given routinely, as well as the majority of the teaching which of course would be technique based.
I rarely to never see this mentioned, mostly because most piano teachers can’t do it. If this were considered part of the standard pedagogy, most teachers would be disqualified. Tough.