For general information, I got word from the Carolina Mountain Club about that area of the Mountains to Sea Trail.
After reaching Green Knob continue on the MST until until it crosses the BRP at Pigeon Gap. Continue on the trail downhill. Soon it will reach Rte. 276 and cross it. Continue on down until you reach a bridge over a sream called Bear Wallow Brook. This would be your camping area for the night.
Thanks to Mr. Joyce of the CMC.