Full Idea
'Neuron' may be understood as a physiological term or a functional term, so even the Identity Theorist is a Functionalist - one who locates mental entities at a very low level of abstraction.
Gist of Idea
Identity theory is functionalism, but located at the lowest level of abstraction
Source
William Lycan (Consciousness [1987], 5.4)
Book Reference
Lycan,William G.: 'Consciousness' [MIT 1995], p.59
A Reaction
This is a striking observation, and somewhat inclines me to switch from identity theory to functionalism. If you ask what is the correct level of abstraction, Lycan's teleological-homuncular version refers you to all the levels.