Take a dowel rod, (one that fits well in your hand) probably around 1/2 inch to 3/4 inch in diameter, cut off about 4 or so inches. Then cut out of that a smaller piece about 3/4 inch tall. The little piece will be the knob and the longer piece will be the handle.
In the handle drill a hole (big enough for the jacket to fit into) all the way through it. It may take some tries to drill it, flip it over then drill again, to get all the way through. Push the jacket into the handle a good ways into it, if not all the way. If it isn't tight and moves around then glue it in place. The jacket needs to be stationary.
If you are going to glue it, I like the two part epoxy. It comes in a double syringe type thing. Mix the epoxy according to the package and when it is thoroughly mixed, pull the jacket out a little and put a dab of it at the bottom of the handle. Then push the jacket back in.
Don't do this near where the cable comes out or you will end up stopping your cable from moving. Only epoxy the bottom of the handle!
Put a spring over the cable. Depending on the thickness of your cable you might be able to take a spring from an old ballpoint pen. You don't want anything too strong (like a trampoline spring.) This is just to return the head to the normal position instead of being stuck looking at the ceiling. You can find springs at a hardware store. Experiment with different springs until you find one you like. Just don't glue the knob on until you are sure.
In the knob, drill a hole just big enough for the cable to fit into. Don't drill all the way through. You just want enough to glue the cable into it. Then glue the cable into the knob. I recommend turning the knob upside down putting some glue into the hole then inserting the cable. Be very careful not to get any glue down into the jacket.
I know you are going to want to test it and make sure it works. Don't do it until you are sure the epoxy has cured all the way. There will be endless amounts of time to test it once the glue dries. If you try and test it before it is dry it will gum up inside the jacket and you will have wasted your time.
Don't give in to the temptation!
Once it is dry you should be able to easily turn your puppet's head, or push down on the knob to make the puppet look up.
In Some of the coral I made for VBS I had a question if I drew stuff free hand or had a pattern. The answer is both. Some things I do without a pattern, but if I have to make a shape that is the same on both sides, I make a pattern.
In this one I needed to make a bumble bee. So I started off with a roll of thick brown paper. I believe they sell this stuff at Home Depot in a roll.
I drew half of the bumble bee on a piece of this paper. Then I cut out the half I had drawn. Then I folded it in half and drew and cut out the other side.
Then I opened it up to see if it was going to fit with what I was needing.
It did. So I wanted to see it with some stripes.
So I added stripes.
Now for the wing. I drew a rough shape...
Then cut out just the part I had drawn. You can see that the other part is square.