I think a 'thoroughgoing functionalist' wants to go further, and say that a person's mental state is somehow constituted by (or reduces to) the functional state of their brain.

Then it's time to return to the rest of your comment - the whole discussion so far has just been about that one claim, that something can be neither conscious nor not-conscious. So now I'll quote myself:

The property dualism I'm talking about occurs when basic sensory qualities like color are identified with such computational properties. Either you end up saying "seeing the color is how it feels" - and "feeling" is the extra, dual property - or you say there's no "feeling" at all - which is denial that consciousness exists. It would be better to be able to assert identity, but then the elements of a conscious experience can't really be coarse-grained states of neuronal ensembles, etc - that would restore the dualism.