The neutral third is a staple interval in Arab Music, but it rarely occurs in western music. It is almost exactly halfway between a major and minor third, and is aptly named, as an ear unfamiliar with the interval will often hesitate, perceiving it as having some qualities of both major and minor thirds. The neutral third is usually perceived as more dissonant than major, minor, or septimal major or minor thirds, but less dissonant than seconds.
In 31-ET, two neutral thirds can be stacked to make a perfect fifth. And, as would be expected, the neutral third can be created by stacking a whole tone and a neutral second.
Since it matches the 11:9 ratio of the harmonic series, the root of a neutral third in 31-ET is usually perceived as a whole step below the bottom note of the interval. However, this interval is rather weak, as these ratios are high up in the harmonic series, and this root will usually only be perceived if the overall harmonic context fits with this root. This can produce all sorts of complex ambiguities.
For example, a neutral chord made out of two stacked neutral thirds, producing a perfect fifth, sounds relatively consonant, but it is usually perceived as having the bottom note as root: the fifth powerfully defines a tonal center, and makes the neutral third function as a slight dissonance rather than defining a tonal center of its own. This effect is similar to the effect of a regular minor chord, but produces a stronger dissonance. On the other hand, stacking a neutral third on top of a whole tone produces a good match to the 8:9:11 harmonics, and thus would imply the bottom note of the whole tone as the root. Another way to reinforce the root of the neutral third would be to stack a neutral third on top of a perfect fifth: this would match the 6:9:11 harmonics, implying the un-heard note in the position of the 4th or 8th harmonic as a root.