Not sure but I think that line is the float bowl overflow. That would indicate that the float needle is leaking past, not uncommon for one that's been sitting. Turning the gas off at the tank and running until the bike runs out of the gas that's in the float bowl and line, then turning the gas on again, may clear debris trapped between the needle and seat. Not too hopeful but sometimes it works and costs nothing to try. Otherwise, take carb apart and clean out. That might not be a bad idea because the idle circuits plug easily and they won't usually clear out on there own. Hope that helps.
Keeping the "Hap" in "Happy Holidays"!
Regime change begins at home.
Blind patriotism is worse than no patriotism.