Country folk tend to like the independence offered by their cars, so how do you get them to use public transit? The Monocab system may be the answer, as it utilizes individual on-demand pods that travel on existing abandoned railways.
I could imagine an autonomous, on-demand rural train service. Due to the low expected traffic, it seems like you could just build some additional sidings and use a more conventional design.
If someone was willing to invest into building and maintaining infrastructure there would be no need for this concept, but that's a political issue. The idea of this concept is do make the best of what you have.