A very good question. Really very good. I can't prove that I have free will. Not directly. However, if we don't have free will, then we can't reason, because we would have no power to reject invalid conclusions. We would be no more free than our calculators, which provide only the answers they are constructed to provide. Therefore, if we are to conduct ourselves as if we were rational beings, we must assume the existence of our free will as an axiom. This is an axiom of absolute necessity, and not one which is adopted arbitrarily; because without such an axiom, all rational thought becomes impossible.
In other words, if we don't have free will, then I'm just typing these words mindlessly, like a music box plays the tune it's been built to play; and you should pay no attention to me -- and I should regard your words as equally meaningless. But we're both assuming otherwise, aren't we?
Interesting how these things cross on a topic. The same idea (that our very actions in posting here indicate we are prepared to make certain assumptions about the universe) you describe is equally applicable to the creationist arguments that we do not truly understand the universe and cannot know anything. (i.e. snow, history, whether the sun will rise tomorroow) That line of inquiry leads to solipsism, which would demand a rejection of interaction with the universe because it is all a figment of the imagination (sorry Descartes) - yet the creationist speaks and posts and therefore proves that solipsism has been rejected.
I'm not asking for proof you have free will. I'm asking for "objectively verifiable evidence in support of your theory that some living beings have free will".
In other words, if we don't have free will, then I'm just typing these words mindlessly, like a music box plays the tune it's been built to play; and you should pay no attention to me --
The conclusion that I should not pay attention to you if you do not have free will does not follow. I can pay attention to a music box (or a CD player) although it is mindless. I can pay attention to and study the weather although it is mindless. I don't need to assume you have free will to pay attention to your words.
Again, what objectively verifiable evidence can you provide that would give plausibility to the theory that you, or any living being, has free will?