Privileged ${\mathrm{S}\mathrm{L}}_3$-local systems are motivic

Let $X$ be a smooth projective variety over the complex numbers, and let $\mathbb{V}$ be an irreducible privileged ${\mathrm{S}\mathrm{L}}_3$-local system on $X$ in the sense of Esnault and Groechenig. We show that $\mathbb{V}$ is of geometric origin. We also give an example of a privileged but non-rigid ${\mathrm{S}\mathrm{L}}_3$-local system.