East Fork of the Illinois Bayou: FR 1301 to Lindsey Mountain Way Road is a 10 mile trail located near Rueter, Missouri. The trail is primarily used for whitewater kayaking.
I've spent a lot of time in the section of the Mark Twain NF shown on the map for this. The trail and roads described here may be misplaced on the map. I never met anyone kayaking in there but there are a few creeks that run through it, they're mostly wet weather creeks. I suppose one could float them after a good rain. There are no backpacking trails in there though. At least not that I'm aware of. But you can backpack anywhere you want to there. I've bushwhacked all over in there.
There are some very nice ATV and 4Wheel drive trails back in there. They can be accessed from the Glade Top Trail road, but they're narrow with lot of brush and tree branches so it's pretty much ATV or jeeps only. It's a long way downhill to find water sources from the Glade Top Trail road if you backpack from there, but the water is good once you find it. Depending on the time of year there will be springs flowing from the hollows.
My advice is drive the Glade Top Trail that's north on Hwy 125 and take a look down into the valley below. There are some very scenic views from there and if you get an itch to backpack down there go for it, it's pretty sweet.