Conjecture on connectedness of Morse boundaries of right-angled Coxeter groups

Let $\Gamma$ be the defining graph of a right-angled Coxeter group $G_\Gamma$. An induced loop $\sigma$ in $\Gamma$ has length greater than $4$ and its vertex set contains no pair of non-adjacent vertices of an induced $4$-cycle in $\Gamma$. Morse-boundary connectedness conjecture. The Morse boundary of $G_\Gamma$ is not totally disconnected if and only if $\Gamma$ contains such an induced loop $\sigma$. The preceding corollary proves the sufficient direction; the converse, characterizing all right-angled Coxeter groups with Morse boundary not totally disconnected, remains open.