Regarding proof of the existence or non-existence of "free will".

It seems to me that to debate the existence or non-existence of free will is a category mistake.
There are no aspects of the concept that can be said to have being; it is merely a way of thinking.
It is possible to say something about the validity of the concept of free will. It is either meaningful or it isn't.
But meaningless isn't the same as non-existent.