My tought would be that "mind" (which is discussed elsewhere) is an emergent property of many brain processes.
We might be conflating mind and consciousness here or even consciousness and "I". If consciousness is just another one of the brain processes that go on then it may well be separate (as indicated by those experiments) from something like "will".
Let me see if I can unconfuse myself here:
We seem to be stuck on thinking of ourselves, the "I" as being a little homonucluum sitting in control of everything. Perhaps like a hydralic shovel operator sitting just behind our forehead and pulling levers etc.
We then use a word like "mind" or "consciousness" and have back in our toughts a picture of this little guy in control. Perhaps this is not the right picture. Perhaps the guy who is pulling the levers is NOT the guy who sits in the box up front and can see what is going on.
Maybe how minds are more like an ant nest. All the different parts react to the various stimulae and do what is needed. Then we have one addtional property. We have something that is aware of the whole thing -- the consciousness. But it is only "being aware" not actually doing anything.
Now I'm sure that this is wrong and even if it contains a grain of truth it would by no means that simple. One would expect that the consciousness
does have some feed back into the various parts that are 'doing' things. That feed back is where something that might be called free will would come in.