It took over a week, but I successfully made a starter from brown rice flour. It followed the same progression as a wheat flour starter, smelling unpleasant (but not revolting; I didn't get the vomit smell) for a few days and then suddenly exploding with activity. Lowering the hydration to about 80% made it look more active. 100% is probably too much for a non-gluten flour.
I used it last night in my first sourdough gluten-free bread, and the tangy flavor really improved the overall flavor. Using 50/50 tapioca starch/brown rice flour I had a decent crumb (for GF, anyway) while also minimizing the strong rice flavor. Definitely a good starting point for more experiments. I hope I can keep it from becoming soapy (colored bubbles and astringent smell) like my white flour starters (3 so far) did. My whole wheat flour starter didn't do that, so I'm hoping the whole grain brown rice acts more like that.
The left container is the original container where I cultured it. The one on the right is half an ounce of the starter on the left plus an ounce rice flour and 0.75 ounces water about two hours later in my fairly warm kitchen.