Phineas Gage & Gremlin in the watch?

Surveying the case for physicalist, what happened to Phineas Gage? Suppose there is a one-to-one correspondence between two things, such as the temperature of a bowl of water and its mean kinetic molecular energy; that is, the temperature and MKE are identical. Now suppose there is the same kind of correspondence between mental states and brain states. For example, whenever I feel a particular sort of pain, there is a particular sort of firing in my brain. Wouldn’t the simplest explanation be that the pain sensation is identical with the firing? Why suppose there is some mysterious private entity that does nothing at all. Illustrate this point with the story about the gremlin in the watch.