Russ, you were on the now unmaintained and therefore unidentified Defeat Ridge Trail. Its winding path to the AT can be seen on the Wear Cove and Thunderhead Mountain quadrangle maps available in print at Sugarlands Visitor Center and online as free downloads at http://store.usgs.gov/
As is the case with the couple of hundred or so similarly sized streams, Thunderhead Prong is not, as you say, labeled on the Trail Map. A few more streams are labeled on the map on the back of the free Fishing Regulations brochurem but not TP. There are about 700 streams labeled on the many quad maps that cover the Park. Others still are indentified on the old historical maps.