Gorenstein pattern-avoidance conjecture for $(p,2)$-clans

Let $\gamma$ be a $(p,2)$-clan with $p\geq 2$, and let $Y_{\gamma}$ be its orbit closure. Gorenstein pattern-avoidance conjecture. $Y_{\gamma}$ is Gorenstein if and only if $\gamma$ avoids the patterns $1++-1$, $1-++1$, $1++221$, $122++1$, $1+212$, and $121+2$. The conjecture holds by computation for $n\leq 7$, while the source states that no ordinary pattern-avoidance characterization exists when $q>2$; the general $(p,2)$ assertion remains open.