The first mistake is to exclude the brain from the body. The brain is just another part of the body. It doesn’t live in a universe of its own hermetically sealed off from the body. It is the body! Every region of you is you. Certainly, some regions (I hesitate to use the word “parts“ with all its mechanistic baggage) are more critical to your existence and operation, but that doesn’t have anything to do with your identity qua identity. The brain is seamless with “the rest”, and in a state of mutual and coherent dependence with “the rest”.

(Now, I can argue that the intellect as abstracting faculty is not material, but this faculty is not disconnected from the brain and needs the brain to operate, and so again, the health of the body affects even those faculties which, strictly speaking, are not bodily per se.)