Here is an update: This is a private arrangement for tutoring so there is no "supervisor" to report to. I encountered the dad outside as I was arriving at their house last Thursday and asked to have a word with him. I explained that his son was developing the habit of putting his hands down his pants during lessons and that I didn't know how I should deal with it - ignore it, tell him not to do that, or let his parents speak to him about it? Dad replied that they had been struggling with that as well. They had come up with the tactic of using a hand gesture of an open hand, palm up, flipped upwards, to indicate that he should get his hands out. He said that it generally worked and seems more effective than a verbal instruction. He didn't seem to be taken aback by the conversation or to regard me as suspect, but rather appeared to take a "we're all in this together" attitude. It turned out better than I had expected. Later, as we were reading, the son started getting his hand in there again several times and each time, when I gave the sign, he pulled out. Success!
As to why we read Greek classics and Shakespeare, the answer is twofold: they are part of the curriculum, and the kid enjoys them. Just because a person cannot control his/her actions, it does not mean that they are not intelligent. He is on the autism spectrum and is nonverbal. He does a lot of pacing, spinning, waving his arms, and humming or repeating certain words or phrases. He cannot focus on a page long enough to read a text. He has a very difficult time communicating through a letter board or keyboard and writes few words and only with extreme difficulty. But he does register enjoyment or displeasure and expresses humor and dislike and FRUSTRATION. I can not imagine what it must be like to be in his situation.
Thanks again for all the responses.