UPDATE: Rotating the geometry so that all of it was in the positive Z dimension seems to have cured the problem. It now renders as expected both with fingers on the screen and off.
All geometry in the prior "black" renders was in the negative Z (due to file exchanging with a Solidworks user). I had simply rotated the CPlane in Rhino for convenience, then opened the file in iRhino.
Did not test this behavior with any other files, but if negative Z renderings are black as default behavior for iRhino, a "Feature Request" would be for negative Z objects to render properly by default. Or, if there is some good reason for this (not sure what it would be, but maybe?), perhaps a setting to permit proper negative Z renders in iRhino Prefs would work also.