They may only be attained during the Tai Bwo Wannai Cleanup minigame, or by purchasing one from another player. You can also get one after clearing/harvesting herb patches if you have purchased the Scroll of Life from Daemonheim Rewards, although this is random. Sometimes after hacking down jungle during the minigame, players will receive a message: "You hack away the remaining bush to reveal an unusual plant." The unusual plant only has an examine option, which reads: "Many plants such as this usually have exotic tubers." Using a spade on the plant gives the player a tuber. (The spade from your Tool beltwill work.)
A similar item to a Gout tuber identified as a Goutweedy lump appears in My Arm's Big Adventure when a human was boiled into a stew along with a lump of Gout tuber he possessed, the man was eaten but lumpy remnants of the tuber can be found in the Cooking Pot at Death Plateau.
If more than one person starts digging up a gout tuber random event at the same time, both players will dig up a gout tuber. You can do this with as many people as you would like! It is advisable that you go with a friend and share your Gout Tubers so both of you can have many more than if only one went.
The Gout tuber is apparently a cheap resource to the villagers of Tai Bwo Wannai. This is evidenced by the small price difference, what can be assumed to be the material cost of the machetes, between Safta Doc and Gabooty. The difference is 200, 400, and 800 Trading Sticks for opal, jade, and red topaz machetes respectively. This may be caused by Safta increasing his prices for your special order, but that would be cancelled out by Gabooty also marking up the price of his items from the price he buys them. If you convert trading sticks to coins using Grand Exchange prices and subtract the low alchemy price of gems (low alchemy because Safta could be able to get a discount from Shilo Village), gout tubers seem to be priced at below 10,000 coins. The variation in price is most likely due to higher labor costs for working with materials that require higher skill.