Once I switched to an aftermarket gas cap, all of my fuel dribble problems went away. I routed all lines to a piss bottle when I had the factory cap still installed. I used an aluminum bottle, but I digress.
With the stock cap it would gather fluid. Aftermarket cap, it's bone dry. Check ball or no check ball, it didn't matter.
I switched to the LighTech gas cap so I could use the Ripper fuel spout which was recommended by
@craig bush and is an amazing product. No ....... around with funnels or tubes.
The only thing I wonder about your setup is venting fuel vapor inside of the fairings. It's almost a bomb until it encounters an ignition source, then it just becomes a bomb.
Where is this hose routed to?
Is this the vacuum line?
To double check about compatibility with fuel in the left coolant tank, there should be a number with triangular arrows around it molded into it. A Google search of same would reveal chemical composition, a subsequent inquiry would reveal resistance to solvents, i.e. gasoline.