I don't think the eye movements in stuttering have anything to do with the frontal lobe. A study in University Texas showed Micro expressions and micro saccadic eye movement occurred during speech preparation preceding stuttered events but not before non stuttered speech. This suggests that before a stuttering like moment there is incomplete inhibition of an unconscious movement, resulting in unconscious eye movement -no frontal involvement until we try to make sense of what is happening [Multimodal explainable AI predicts upcoming speech behavior in adults who stutter - PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC9376608/) Did you know that your eye movement and tongue movement are unconsciously connected?