I would really recommend the McGuire Program! And reading Redefining Stuttering by John Harrison. There’s a free link to the book if you google search it. Your head jerk is a “trick” to get words out. Our bodies sometimes do involuntary movements to distract us from the stuttering, which allows the word to come out. The way to reduce tricks is by reducing struggle, and by not rushing your words out. And you can reduce struggle by “block releasing (letting out a repetition and then starting the word over again.” Here’s a good example. https://m.youtube.com/watch?v=UA4ZhaZ-zV8&t=256s Ultimately this head jerk started as a way to either avoid stuttering, or to avoid making the listener wait longer than they would for a fluent person. Then the head jerk became a learned behavior because it helps you not stutter. Stuttering is all about internal tension, and if we don’t allow ourselves to stutter openly, then the tension will manifest in our body. If it takes you 5 repetitions to say a word, then do that. But if you try to take that same word and force it to come out fluently, you will have tension and that causes the head jerk. So don’t force fluency, speak with repetitions if you have to.