This is something I have thought about a lot.
Something that I am doing recently is really trying to listen to my inward self. I will get a kind of "welling" inside which I have recently been aiming to define in pitch, vs. allowing it to stay as only a welling within. This is not always easy. Once I can find that, though, I find it on the piano. There are, in fact, particular characteristics which would help you know what it is, but right now I am not always finding a starting pitch at a first try. And, this is different for me right now than worrying about if I were able to name a random pitch in the air while other people are watching. This is personal.
Today, I listened to myself and sat down to play what I heard and out came music from within me in a defined way. Just about half and hour ago, I once again heard music within me which also felt like a welling, and I sat at the piano trying to hear this and find it on the piano. Now, this may not seem like much, but something that I think is very interesting is that, what came out of me this evening started off being quite mysterious to me. I couldn't quite hear all of it, but then I started to hear more and more, and do you know what happened? A piece that I had started composing about 4 months ago, but never recorded or wrote down and had basically forgotten about altogether, came right out of me, in the same key (I remember now) as what I had orginally been composing it in. So, it started as a welling, I listened for the definition, and aside from having stumbled again upon the text --which, if there wasn't something specific to the sound, could have been anywhere-- I found it in the exact right key by "accident" (no fishing).
I think that's interesting.