With the bike on the side stand and the gas cap open, you can see the drain on the left side(looking down from the top), that is the drain should you over fill(you can see the holes thru the cap assembly. The rear, with the red seal is the vent.
The pic Randy posted is my spare tank with the pump out showing each of those lines
Agreed, it sounds like one of those tubes are leaking which is very unusual (unless you have a bunch of rust inside to start with).
**What you may try doing is fill the tank to the top.
Remove the gas cap, (3 bolts outside, one under the open cap).
Then, put some
air pressure ONE at a time, at the bottom of the drain hoses, maybe 5-10 PSI, while holding a finger over the appropriate hole(pressurizing the steel line) at the top.
IF, one of those internal lines are leaking, you'll
get all kinds of air bubbles coming up to fuel cap opening. You shouldn't get anything.
(With loosing approx a gallon, that leak is towards the very top, a gallons worth of fuel obviously)
If you do, it time to pull the tank, pump and inspect. If the inside is in good shape and there is a hole in one of the lines, to save it, you may be able to save it with a
split fuel line hose and a hose clamp around it or some fuel resistant epoxy. If the
fumes can be removed fully, depending on where the leak is,
brazing the hole, (sounds small from what your posting and about in the middle of one of those lines) is possible.
BTW, both those lines, at the bottom, have a white stripe of paint on the bottom. They should exit on the right side near the O2 sensor. There's an actual plastic round piece the hoses go thru to keep from flopping around.
As Randy posted, they shouldn't be kinked (it'd screw up the test too). You can easily, follow both rubber hoses down from the tank (bike fully assembled) (I touch mine with a finger and tug feeling the line so I know I'm on the correct line) and gently tug on the lower end of the hoses. The left side hose should track off from the left to the right side and go into that plastic retainer.
For the S1 bikes, the radiator overflow line comes out thru there as well (3 lines). Your should see two if the lines are routed correctly.
Just a larger, easier pic to see:
In this pic, you can see the two lines(holes for venting/draining and 4 bolt holes for the cap. Again, one bolt is UNDER the open cap. The six bolts showing on the outside, 3 work, 3 are just for looks..