What physical interaction mediates this transmission and reception? Where's the evidence for such an interaction? Where are the specific transmission and reception sites in the brain? Why haven't brain anatomists seen such sites?You are begging the question. If the soul exists, it would be, as traditionally stated, the substantial form of the body. He is not really proving immortality but existence "outside" the body. Apart from the body, the soul would "fade away" as dissolution takes place. This is Aristotle's view. Plato's view is that the soul is something that exists before the body takes shape and will survive it.
I don't think I was begging the question so much as attempting to elicit a response that had some hope of making sense from an empirical point of view. The brain is a physical object and if one claims that it's serving as some sort of receiver or transmitter of information, one ought to be able to say something meaningful about how that process takes place physically. If, as you suggest, reversion to a pre-scientific notion of 'soul' is the issue, none of this has anything to do with medicine or science at all, and so the fact that it is a medical doctor who is making the claim is irrelevanthe is not making the claim qua physician.