It's about 2/3 of interest for me. It's very hard to tell with young beginners; kids who are 4 or 5 will do as they're told; they always have pretty easy going personalities and will try anything you throw at them
I kind of 'trick' some of my students in a sense lol. The ones who started early enough to be able to get a grade 12 high school credit for piano, and use it for university, are pretty keen on getting the exams done and possibly having an easier last year of high school. So I'd say all the kids who are learning pieces for exams are pretty into it. Kids who are learning pop and classical are playing a pretty large variety, and really enjoy it. All of my adult students are there for their own leisure, so obviously have to be interested to a degree.
The one's I have who aren't interested are the ones who play random stuff, don't want to do exams, have no musical preference whatsoever, have parents who often forget to take them to piano, forget to pick up books, don't want to buy books, etc. These are usually the kids who are 8-12. The preteens who just don't care, don't open up to the teacher, low energy, always seem bored no matter what. It's tedious teaching them, because you know that they really don't care at all.