Now that’s a question and a half. I think intrinsic motivation is not remotely studied enough to be able to give an answer to that. Most of the time, in practice, we simply observe it, or ascribe people’s non-incentivized behaviour to it.
It is only a hunch, but I think that agency plays a role, possibly an important role even, in intrinsic motivation. It’s the kind of thing I notice in my work in organization development — when people feel they have that agency, that they can exert some control over what they do, connect it with an inherent personal motive, have freedom to determine how they do it, they will display more inherent motivation.
I suppose creating the conditions in which that can happen is in effect an extrinsic intervention.