Hydrolic clutch line. if its leaking you probably put a crack in it. replace it
yup does seem to b an overflow line trying to check it on mine but its 2 hot outside + bike is hot, looks like it T's off to that brown hose could b wrong thoif you are refering to the tube that has an open end in the picture I think that is a overflow "tube" from the tank, and unless I am mistaken and I could be there should be a T union on the end so that the excess fuel will exit under the bike and not on your leg. Thanks for pointing that out Henessy
^^^ +1...what he saidno its not always open but when you laid it down the T union could have popped off and that is probably why its open if you follow the tube that runs down just pass the your slave cylinder you might ba able to see if it is disconnected there