Effects of tongue position and jaw position on the postural control system has been a subject of study in many researches. Both the positions have been found effecting the stability.
Mastication of chewing gum improved the postural stability during upright standing in some studies. Explanation may lay in activation of mastication muscles, condition of temporomandibular joint and trigeminal proprioception. I suggest this study to confirm the opinion:
Article Effect of masticating chewing gum on postural stability duri...
It is, and there are more studies about this around.
Article Effect of chewing gum on static posturography in patients wi...
Article Effect of chewing on postural stability during quiet standin...
https://publikationen.bibliothek.kit.edu/1000082693/13185666 clicking on this last one downloads the article. I speak to many SLP's and they are very aware of this mechanisme.
Chewing gum for relatively long periods could harm the masticatory system causing temporomandibular joint dysfunction and masticatory muscle spasm in susceptible individuals.