The K bike K12/13, don't have a stand tube like older style bike fuel systems where you rotate a petcock to reserve and now have access to the last of the fuel. BMW just says reserve, meaning a point at which the yellow reserve fuel is now being used. It is all one large sloshing gas tank. Also your bike has only a fine mesh shock at the fuel pump intake. You probably already have but if not, it would be a good idea to research how to open your tank up (off the bike) and dump out everything and clean the tank with some fresh gasoline. All a big mess to do but worth it. So it is possible for this to build up a little before you reach the suction of the pump but not much. Time to think about both your lid seal and where you purchase your fuel.
Mount Vernon, WA.
tire guy, I'll mount your tires.