How can I prevent water trail stains on bathroom drywall?
As Kris said in a comment, the solution is to not let that much moisture accumulate. Run a well-performing bath fan every time you use the shower, even in the dead of winter. Vary run duration accordingly. In my part of the world this means 2-4 hours in summer and at least a quarter of an hour (after the shower ends) in winter. 

As I often say, your bathroom isn't a bathtub. It shouldn't be expected to hold water, whether on the floor or the walls.