I have just started my vulcan1500 which has not been started for about 2 months, it has been stored covered in my shop.
Upon starting it I found gasoline running from a rubber tube located and ending under the seat on the left side of the upper frame, it appears to me to be an overflow of some sort. When the bike is running the flow is quite substantial.

that tube is definately an overflow. The carb has a built in fail safe that overflows excessive fuel so that when sitting that fuel doesnt flow into the motor causeing possible damage.
what this means to your bike is especially after any kind of storage over a few weeks, parts in the carbs start to get a little builup. In this case the float valve has gotten some builup and is causeing it to hang open, allowing alot of unwanted fuel.
Sometinmes if your lucky just a couple of slight tapping on the carbs can help rid this. Or completely drain them can help jar them loose again. But if you cant get any results from this.
The best way to take care of it is get the carbs off and have it cleaned.