Realizability conjecture for sign patterns with positive pairs

A sign pattern is a sequence of signs, and $(pos,\neg)$ denotes the associated pair satisfying the standard condition

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Realizability conjecture. For an arbitrary sign pattern ${\bar \sigma}$, the only type of pairs $(pos,\neg)$ which can be non-realizable has either $pos$ or $\neg$ vanishing. Equivalently, for any sign pattern ${\bar \sigma}$, every pair $(pos,\neg)$ satisfying the standard condition with positive $pos$ and $\neg$ is realizable.

The claim is motivated by the computer-aided classification for $d=7$ and $d=8$: all listed non-realizable or unresolved examples have at least one vanishing component. Its general validity is not established in the supplied text.