Our body reacts to smell, sight and touching of foods, but the effects on the triggering activation of digestive system are minor. But when any food or food like substances go in our mouth, the digestive system thinks the food is coming in and then there is none. Toothpaste or vitamins will do that.
Brushing with water is not a bad idea. Scrapping your tongue with a tongue scraper is also good, even when you are not fasting.
In my early days of fasting in my youth I used to use Sea Salt to brush my teeth and all experts I spoke to made me stop that.
I do not have a proof of comparison of what were the downfall of using or not using toothpaste or Sea Salt .