You are leaking gas below the scooter even from a nearly empty fuel tank?
There are 3 hoses up there on the fuel tank.
An overflow hose, a vent hose, and the line taking the fuel to the engine.
There really is no 'breather tube' subject to leaking - just a hose to your sneaker tops if you're standing there over-filling the tank at the gas pump.
THE OVERFLOW HOSE:
OK, the "overflow hose" is connected to the rubber tray which is next to the gas tank opening. It is simply there to drain off, below the scooter, any gas you spill when filling - or if you overflow the tank opening itself. This hose is hard to see if the under-seat bucket has not been lifted out. It is connected on the left side of the rubber cup. (same side the side stand is on)
I doubt you are leaking gas from this hose - opening the seat would show you a puddle of gas sitting in that round black rubber tray, waiting to drain off.
THE VENT HOSE:
This vent hose is the one connected directly to the filler neck, just below the gas cap. It is not meant to have fuel in it, ever. It is NOT an overflow hose.
Since you have a history of overfilling the tank - you likely now have fuel through this hose into the emissions and venting system ( which has a one-way valve and a canister in the system of hoses on the front of the tank - visible when you pull the underseat bucket) This hose/vent system is meant to take the fuel tank vapors to be burned in the engine. I think.
I guess you could have fuel in this system which is now dripping out.
You could remove the seat bucket and study these vent lines - I removed and cleaned mine out one time - getting that valve working again by sucking and blowing. Take a picture of the hoses so you can replace them properly. Shake 'em out, gently blow out any fuel from that acorn sized valve case.
Still, hard to understand how a nearly empty tank could have fuel raised to the tank neck to enter this system?? Is there a vacuum when you open the gas cap, ever? It is meant to inhale - does it? Mine got stopped up one time. I used compressed air to clean it out.
THE FUEL LINE TO THE ENGINE:
This might be the best place to find your fuel leak. Please remove the seat bucket.
Starting up on the tank, look for a leak from the fuel line connection at the nipple of the fuel pump, down to where the fuel line ends at the injector.
Is the area around the injector wet? The fuel pump is under that silver disc with the 6 golden bolts. Any wetness around that silver cap, or the hose connection?
Yeah, your carb drain isn't leaking - nor is your float stuck. You have fuel injection.
Hope you tank isn't leaking - that would be a first.
Please take a look again - and tell us what you find.
Stig