All our real insights on this matter come from experiments involving amputations or lesions, like split brain patients, quadriplegics, Phineas Gage and others. Split brain patients are essentially 2 different people occupying a single body. The left half and right half can act and communicate independently (the right half can only do so nonverbally). On the other hand you could lose all your limbs and still feel pretty much the same, modulo the odd phantom limb. Clearly there is something special about the brain. I think the only reasonable conclusion is that the self is embodied by neurons, and more than 99% of your neurons are in your brain. Sure you change a bit when you lose some of those peripheral neurons, but only a wee bit. All the other cells in your body could be replaced by sufficiently advanced machinery to keep all the neurons alive and perfectly mimic the electrical signals they were getting before (all your senses as well as propioception) and you wouldn't feel, think, or act any differently