How do you count sugar free gum?

I don't

Reportedly, an average stick of sugar free gum has aound 3-5 calories. It should be possible to find the number of calories in the specific gum you're chewing, if it's a mainstream brand. In the US, it should typically have a nutrition label that states the calories per serving. In my understanding, in the US, anything that has fewer than 5 calories per serving can list zero calories on the label.

Honestly, unless you chew a huge number of sticks of sugar free gum, the calorie impact of a stick of gum is so small that it would be lost amongst the variation from unavoidable errors in logging. (I'm talking about things like one apple being sweeter than another when of the same weight.)

There may be reasons to avoid chewing lots of sugarless gum, such as that some types contain sugar alcohols that cause digestive distress for some people. Some people are more sensitive than others, and the more a person consumes, the more likely anyone may be to experience some effect.

If you want to track how much gum you chew for reasons like tracking sensitivity levels, then just count how many sticks you chew in a day, and log them.