Schoolhouse Falls is in King's Cove.
About a year ago, I tried to get there from the switchback on Road 208 like you were going to Riddle Creek. I had some old directions that I found on the internet that referenced an "old road bed" and an "obvious trail" both going in a a southeasterly direction, neither of which I could find.
That's the way we went. Walk about 100 feet north of the parking area at the switchback and you should see the old road and a faint trail. We followed it until it split. From here we continued in the general direction of where King's Cove should be, which is, as you said, a southeasternly direction. We then went down a drainage and came to the top of Schoolhouse or King's Cove Falls. There is no easy way down. We went to the right.
This is approximately the coords for the falls 34.3271703, -87.473359