This was happening on my old pan, and like you say, it drips from the plug. It wasn't til I read about the rock shield here on Mud that I figured out what was going on.
When I finally pulled the old pan, there was RTV inside, dabbed on all of the tack welds that hold the rock shield in place...
Something to think about - if your oil pan is original, the plug above is great. I used one for years. The fact that it works across the diffs and tcase is a bonus.
But if the pan has been replaced with new OEM semi-recently, the drain plug size will be different (smaller). My replacement OEM...