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@JohannesHuisman: That's what I meant, and I hope it was clear from the context. It would be perverse to take a trivial local system that also happened to be a module over the fundamental group...
@TylerLawson: That's a good example -- I thought I had worked out $\mathbb{Z}$ acting on $\mathbb{R}$, but looking back over my notes I had screwed it up. Still very interested if you ever figure this out.
