Two kilometres north of Muang Khong a trail leads to Green Mountain Cave, a small, shallow shelter in the middle of the forest. It holds some fairly crude Buddha images and bits of broken pottery and is the object of an annual pilgrimage, usually in June. It's definitely more about the journey than the destination.
It's only a 15-minute walk, mostly uphill. Follow what is clearly the main trail to the second rocky opening in the forest and then veer south (left) to the little cliff. The trailhead is marked by a blue sign. If you wish to continue past the cave to the viewpoint or even all the way across the island, you'll need a guide.