Isolation conjecture for parabolic periodic points in positive characteristic

Let $f$ be an analytic map over an ultrametric field of positive characteristic, and let $\zeta_0$ be a parabolic periodic point, meaning that for its minimal period $n$, the multiplier $(f^n)'(\zeta_0)$ is a root of unity. Isolation conjecture. Every parabolic periodic point is either isolated as a periodic point, or has a neighborhood on which an iterate of $f$ is the identity. In positive characteristic, this conjecture addresses the remaining case after the corresponding isolation result in characteristic zero; the cited prior work proposed it, while the supplied status gives no evidence of resolution.