I finally resorted to examples:
"St. George fought the dragon."
"fought the dragon"
Eventually, First Son seemed to pick up on the idea and could consistently correct his phrases when I pointed out they were incomplete.
I was delighted to discover what is likely the answer to my problem in Charlotte Mason's Towards A Philosophy of Education. I imagine this particular idea is addressed in lots of other books about Charlotte Mason's methods, but somehow I missed it.
Every sentence has two parts, (1), the thing we speak of, and (2), what we say about it.The first part of a sentence, of course, is the subject.
How simple it would have been to say to First Son, "Who or what are you speaking about?"
Now that I think about it, I'm sure I will be saying that to him in the future.