Odd-cycle Maker-Breaker metric resolving game conjecture

Let $C_n$ be the cycle graph on $n$ vertices, and let $O_{R,1}(C_n)$ denote the outcome of the $B$-game of the Maker-Breaker metric resolving game with parameter $1$ on $C_n$. Let $\mathcal{M}$ denote the outcome in which Maker wins.

Odd-cycle conjecture. For every odd integer $n\ge5$,

$$O_{R,1}(C_n)=\mathcal{M}.$$

The claim extends the explicitly verified cases $n=5,7,9$ to all odd cycle lengths at least five. The paper states that a general argument is not known.