Hello Martin:
There is a speciality tool available for cleaning the tube that runs through the middle of the upper gas tank of the ST 1300, from the fuel cap scupper hole to the drain nipple on the bottom of the tank. It's not advertised as a motorcycle tool, it's advertised as a tool to clean Bunn coffee machines.
The tool is a tightly-woven spring that is 20 inches long. It's not expensive (typically about USD $5 to $10), and it's a handy tool to have around the house because it is useful for cleaning out all sorts of tubes - evaporator drain pans on household air conditioners, rubber hoses, etc. You can buy one from a coffee machine specialty company. When using it on the motorcycle fuel tank, rotate (twirl) the spring as you insert it, this enables it to negotiate bends in the tube. You can stick it in to either end of the tube in the tank. It's also useful for cleaning debris out of small rubber drain hoses on the motorcycle.
For reference, here's a link to an advertisement for this tool:
Bunn Coffee Maker Deliming Spring Tool
Michael
Coffee Machine Deliming Spring / ST 1300 Fuel Scupper Tube Cleaning Spring