Take more direct control, but leave it up to him still.
Don't ask open ended questions like "what do you want to do?" - Instead ask yes or no questions, or questions where there is only a couple of possible answers. .. "We're going to learn about a song today, I have 2 to choose from.. play them.. get him to choose.." if he has no opinion still get him to choose in an arbitrary fashion. Just first one or second one with no real reason.
Also, it may benefit you to simply get him talking, this is just a rapport thing.. make sure he is comfortable with you in the lesson. So you can ask him about school, friends? computer games? whatever.. you can prompt answers to, like "I did this on the weekend, what did you do" so he has some idea of what an appropriate response is..
With quiet kids you need to ask SPECIFIC questions, or you'll just get a generic nothing response.. so its not like "how was school?" its more like "did you do any maths at school today?" .. "do you do music at school? whats the teacher's name?" just stuff where there is a really direct and obvious simple answer.. the lesson should feel like you're just hanging out together, but you're at the piano.
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on the lesson front..
If that is exactly how you're getting him to find "C" you are missing steps. Don't worry about middle C, lets just get any C.
Find groups of 2 or 3 black keys, play them.. do it with eyes closed by feel, do it with RH, do it with left hand.
Now say, C is the white key, on the LEFT of a group of 2 black keys.
NO POINTING AT C. He must find it on his own based on your description of its location.
Get him to play ALL of the C's, and say "C" out-loud while he does it. Saying it out loud is important because it creates a mental association between the letter C and the physical position of the key. When you come back to it, if he hits D, dont say "thats wrong" say "I think is close to that, do you remember how to find it? wasn't it on the left of 2 black keys? can you find 2 black keys, now where is the key on the left.. that one is C.
..be prepared to have to remind him which way is left.
Teach these in the same manner, and in this order.
C, left of 2 black
F, left of 3 black
Now test, "find me a C, find me an F, find me a different F, find be a C and play it with LH finger number 2" etc.
E, right of 2 black
B, right of 3 black
test again, adding these keys so now there's 4.
add in other keys, D is between 2 black keys, G and A are between the 3 black keys.