Sure, it's the brain or the physical body in general that's the tool-user. The brain identifies with the mind rather than with neurons because the brain doesn't know itself that directly. Neurons connect to other neurons, but neurons don't mentally represent each other as neurons. Rather, they construct the overall model of the mind/self/person/character. That model seems to do the self-identifying, as far as the conscious self is concerned. But perhaps the true act of self-identification is largely unconscious. The brain's tools would be neurological, and I haven't looked much into that detailed level of explanation. (I'm not a neuroscientist.)

I've explained what facilitates the act of identification. It's like identifying with the car you drive. Overfamiliarity leads to a loosening of mental boundaries, as the use of the extension or vehicle becomes second nature to you.

The computer software image is just a metaphor, and metaphors are free to be strong or weak. In any case, they're limited. But sure, the mind can be regarded as a "state" of the neural hardware. So what? Where else would the mind be?

What percentage of mystics would you say posit spirits? And is there some mystic police force out there that prohibits some theists and supernaturalists from calling themselves mystical?