Hi, if you "always drink tea when" you are fasting, then you are not water fasting--and what you might be feeling falls out of the province of water fasting. You're into the terrain of deprivation. Adding a bit of gum (I hope, and not "gun"!)
just gets the digestive juices going... expecting some nourishment, and/or shutting down to save stores. This is putting the body under stress.
If you then are extremely thirsty, then maybe it's the body's many cries for water--might be a request to actually do a genuine water fast. That's nothing like the extremely low-calorie fasting you are currently doing.