This sounds like it assumes a physical mind could access a non-physical soul. All we probably know is that we have to be using an intact mind to use free will.
That's not a completely watertight argument.
Consider a traditional FM/AM radio. You can modify it, damage it, and get notable changes to its behaviour...
> Of note is anesthesia which can reliably and reversibly stop internal experience in the mind
...turn it off and on again...
> For a non-physical soul to hold our mind we would expect significant divergence from the above.
... yet concluding that all the noises produced from the radio are purely internal, mechanical and physical would be the wrong conclusion.
(I'm not arguing that the human brain/mind is anything like analogous to a radio, just pointing out the limits of this approach.)
Although, sure, if we could somehow manage to determine that souls did exist then presumably an AI model as capable as a human would also be eligible for one.
The effect of drugs (including alcohol) on the mind. Of note is anesthesia which can reliably and reversibly stop internal experience in the mind.
For a non-physical soul to hold our mind we would expect significant divergence from the above. Out of body experiences and similar are indistinguishable from dreams/hallucinations when tested against external reality (remote viewing and the like).