It's very common for people who stutter to display what are called *secondary behaviors* when stuttering. Secondary behaviors are physical actions such as blinking, nodding/head movements, stamping the feet, clenching fists, or any number of other actions. Getting rid of secondary behaviors is often a goal in speech therapy, because they can be quite distracting and usually draw more attention to the stutter, making it seem more unnatural and highlight the "struggle" aspect. From a neurophysiological standpoint, they don't actually assist with getting through the stutter. Of course, many people do this, so it understandably "feels" like secondary behaviors help! Mechanically, there is nothing about blinking or tapping your feet that makes your lips work better, etc.