There is (was) a check ball in the breather assembly in the gas cap. It was removed at one point and there was a service bulletin telling dealers to remove it. I've tried it with and without the ball, no real difference.
I removed the EVAP canister and ran both the overflow and breather tank lines to a catch bottle.
I'd also add that I think the guy here who went with a racing style gas cap don't have the venting/vapor build up problems as they seem to vent straight to the atmosphere. I wouldn't use one if I parked my bike in public places for extended periods of time. The LighTech TFN212 is the correct part for 1199 and newer Ducati bikes that all use the same OEM gas cap. The LighTech is the only one I found which will fit the Ripper gas nozzle, should you like that for track days.
View attachment 45343
These nozzles are a pretty cool design in that they're self venting and will shut off when the tank is full. No hoses or funnels to mess with. Its too big for the OEM gas cap though.
View attachment 45344