This is a very common development in stuttering, and it's probably not a good idea to lean into. Have you ever seen someone stuttering a lot, plus they're also doing unusual little things on top of it like a facial tic or a little grunting or yelping noise or a sudden attack of rapid blinking? This is how those secondary behavior start. You may find some very short-term relief where you slip out of a stutter by throwing your head in a certain direction, but sooner or later your stutter is likely to re-emerge despite the head trick, meaning you'll be stuttering as well as twitching your head.