According to Shelton, no gum chewing during fast. Personally, if I really needed something in my mouth I'd rather chew gum than break my fast too soon with food ha. I think it's OK to bend the rules just a little bit.

"GUM CHEWING

It has been determined experimentally, that the chewing of gum occasions an inhibition of gastric secretion. This, instead of enhancing digestion, as gum chewing is popularly and professionally supposed to do, actually retards the digestion of protein foods. As there is no digestion going on during a fast, it may seem unimportant if the faster chews gum, but this is far from true. I have permitted fasters to chew gum and I have noted a tendency to chew it in large quantities, the faster chewing three or four packages of gum a day. I am inclined to think that he chews it until he extracts all the Sugar from it, then takes fresh gum, doing the same with this.

Gum chewing serves no useful purpose. It is an evidence of weakness, the foundation for which is laid in infancy and early childhood. Mothers give their babies bottles, nipples, crackers or cookies to keep them quiet. Later in life these perpetual sucklings trade their nipples or their cookies for chewing gum or the cigarette. Gum chewing is a mental habit that is needless and foolish, as well as a wasteful practice under any and all circumstances. It is not the innocent practice it is commonly regarded. There can be no doubt that it exhausts the salivary glands. It does not seem probable that any useless habit can be regularly indulged by anybody with impunity. Gum chewing is certainly wasteful of the patient's energy and the energy wasted in this useless practice may be, at least in very low states of health, just enough to mean the difference between recovery and death. It is particularly essential in all serious states of disease, and in fasting, that all nerve-leaks and all sources of enervation be discontinued. Energy must be conserved in every possible way. The faster should certainly refrain from chewing gum."