Interesting. People often when they stutter, do a physical action ( I touch the side of my head and/or close eyes slightly) to help get over a block. Maybe this is your "action". Or just the exercise warm up your mouth and makes the fundamentals easier to implement? People chewing gum have an aura of "yeah whatever" so like you said you could just be relaxed. You could even feel more cool (I tend to when chewing gum) so your speech is better.