The complexity of matroid homomorphism reconfiguration

We consider a reconfiguration version of the homomorphism problem ${\mathrm{H}\mathrm{o}\mathrm{m}}_{\mathbb{M}}(N)$ for binary matroids $N$. This reconfiguration problem, ${\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{l}}_{\mathbb{M}}(N)$, asks, for two homomorphisms $\phi$ and $\psi$ of a matroid $M$ to $N$, if there is a path of homomorphism from $\phi$ to $\psi$ such that consecutive homomorphism in the path differ on a single cocircuit of $N$. We show that this problem is trivial in the case that $N$ dismantles to the graphic matroid $M(K_2)$, and that the problem is $\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$-complete when $N$ is the graphic matroid $M(K_3)$, $M(K_4)$, or any graphic matroid containing $M(K_5)$.