Uhura has nothing to do in the episode because she's a character Roddenberry added when he re-wrote the episode. She got some of the lines that were supposed to go to Bailey.
John D.F. Black's tenure on the show wasn't long. He was the associate producer/story editor for the first thirteen episodes of the series, but conflict with Roddenberry sent him packing. His only writing credit is for "The Naked Time."