The retract-image conjecture for non-bipartite generalized Petersen graphs

Let $G(n,k)$ be a non-bipartite generalized Petersen graph, and let $f$ be an endomorphism of $G(n,k)$. The retract-image conjecture. The image of $f$ is a retract of $G(n,k)$.

The claim concerns the structure of endomorphism images. The source notes that it fails for bipartite generalized Petersen graphs, giving the Möbius–Kantor graph $G(8,3)$ as a counterexample, but gives no resolution for the non-bipartite case.