I don't think there is a neutral state although I'm going to have to go back to Barrett and Lembke to think about this in light of their research. (Sent thoughts, Godfrey ?)
Practically speaking I don't think there's a neutral state.
Neurologically speaking I'm not qualified to answer that. But of course I'm happy to toss out an opinion.
The affective circumplex and the teeter totter are both conceptual models or analogies and therefore it could be assumed that they don't fully represent the biological processes at work. They seem to imply a neutral state at 0,0 or at perfectly level, respectively. But it could be that these implied states are a failure of the analogies, or that they are so infinitesimal as to be meaningless.
This paper is generally...not great (especially with chestnuts like this, implying that the ideal state of a hedonist would be maximum, activated bliss all the time - wearing me out literally just reading the sentence..."For instance, going from a painful experience to a neutral one probably feels like an improvement, whereas going from a joyous state to a neutral one might be experienced as a decline." emphasis mine)
But it does offer a nice overview and lots of links to other sources. The one thing I do agree with the author on, is that the "neutral" affect, if it exists at all, need not be experienced neutrally. My thoughts are that "neutral" states are valenced by our perspective (not necessarily only fleeting momentary moods), which is why an Epicurean can experience hedonic pleasure from them, while a Cyrenaic may try to avoid them altogether, and many other people may seek or avoid depending on their moods, or the amount of "virtue" they place in not feeling much of anything.