I have had sugar free chewing gum aswell, not only does it help to 'chew' something, but also it helps get rid of the motor breath that ketosis gives lol. I do tend to drink a bit more when I have chewing gum, not sure whether thats a mental thing or whether it makes me more thirsty or what actually lol.
Some people say no to it, but if it helps you, then thats fine right? Just make sure that if you do have it, that it won't lead to you wanting to eat some real food and then falling off the wagon.