Why is the drywall wet in one corner?
I'd go with FrK and Steve Sether, since you found no signs of water and this is a bump-out. Condensation is most likely.
It could be a lack of insulation, but more likely it's an air leak. This could be permanently fixed if a Spray Foam's tube easily feeds up into there from a gap in the siding's corner or from drilling a small hole in the room's corner.
You'll need Big Gap Filler spray foam, shot for about 5-seconds to get the area filled.