Thymol is part of quite a few Pharmacopoeias. Usually used as a topical antiseptic for dental work .There are limits as its quite toxic.
You could in theory substitute Clove oil, or rosmary essential oil which is used as a preservative in some natural extracts used in "Preservative free" toiletries products.
Sodium benzoate is a good choice, but can be pH sensitive and either discolour badly or be useless if the pH is outside its comfort zone
0.1% (1g/Litre) is obviously effective as Dana proved, but this material can be used upto 5g/litre routinely if you have a buggy batch of gum powder.
The other way (Which should work for solutions that are prone to bugs (Works for dilute detergent blends, which are bug fodder)
is to adjust the pH to either below 4 with a hint of acetic acid (Stop Bath) or a touch of either sodium or potassium hydroxide to take it above pH 10
I haven't tried this with gum, so I can't guarentee it won't shock stuff out, but at least you don't have to get hold of real nasty stuff like formalin, formaldehyde donor preservatives or stinky oils