It is a Vt 700, not a vf.
That would make it a Shadow, right?
I had the same bike. AAAAAnd it had the same problem. I would check the float hight. The carbs sit at a kind of strange angle, so the float hight is critical. Also the bowl gaskets are always under gas so if there is any problem with those it will leak. Mine backfired real bad until I replaced the cut off valves on the carbs. Other than that it was a great bike. It had a sixth gear overdrive and got 55 to 60 mpg routinely. The tack goes wonky on those, it is a diode in the tach assy. that goes bad. It is an electronic tach. Make sure that you grease the splines on the shaft drive where the drive shaft goes into the final drive.
Al