I agree feedback is a big part of it. For example, the times in my life when I’ve been most motivated to play musical instruments were when I had regular opportunities to play in front of people. Whenever that disappeared, the interest went away too.
But also I think some of it is sticky, or due to personality factors. We could even say it’s not about willpower at all, but about value differences. Some people are just more okay with homeostasis, staying at a certain level (which can be lower or higher for different people) and using only as much effort as needed for that. While others keep climbing and applying effort without ever reaching a level that lets them relax. Many billionaires seem to be of that second type. I’m more of the first type, with many of my active periods being prompted by external changes, threats to homeostasis. It’s clear that type 2 achieves more than type 1, but it’s not clear which type is happier and whether one should want to switch types.
Your examples sound familiar to me too, but after rereading your comment and mine, maybe it all can be generalized in a different way. Namely, that internal motivation leads to a low level of effort: reading some textbooks now and then, solving some exercises, producing some small things. It still feels a bit like staying in place. Whereas it takes external motivation to actually move forward with math, or art, or whatever—to spend lots of effort and try to raise my level every day. That’s how it feels for me. Maybe some people can do it without external motivation, or maybe they lucked into getting external motivation in the right way, I don’t know.