There are two "drain" tubes on the left, underside of the FJR.
One is the "overflow" tube which comes from the well area surrounding the filler neck. The only way that you should see fuel there is if you overfill it (duh!) or if the gasket around your gas cap is leaking.
The other tube comes from the tank vent. This is probably the one that was dripping on yours. The path for venting is through the gas cap itself and into the orange grommet thingee that you see when you open the cap. Inside the gas cap is a check valve and a "restriction" device. When you are driving and using fuel the tank develops a slight vacuum and the check valve opens allowing air to relieve that vacuum. If this vent doesn't work your tank eventually gets sucked in and implodes. This has happened.
When the fuel warms in the tank in the hot sun it expands (are you a science teacher?) and the tank pressurizes. The check valve is closed, so the expanding fuel pressurizes the air and fuel vapors above the fuel. The only path out is through what I called the "restriction device". It looks like a little filter thingee, and it causes a positive pressure to develop before it will allow venting. Some folks theorize that this and the check valve are there to prevent fuel from venting in the case of the inevitable drop.
I have disassembled and modified my fuel cap to remove the check valve, essentially allowing my tank to vent freely. Yes, I am undoubtedly destroying the atmosphere with ventilating hydrocarbons, and am running serious risk of inflammation. I've been told that I will die a fiery death in the event that I dump the bike and cannot extricate myself from under the dripping fuel vent line. But my tank will not implode on itself and will also never geyser up into my face when I open the gas cap at a fuel stop (as some 1st gens are wont to do).
I documented the innards of the fuel cap here:
Click for fuel cap pleasure
Sorry, back to your case of the drip. When you have recently filled the bike (with cold gas) and you will be parking it in the sun, you may consider parking the bike on the center stand as a means to keep liquid fuel as far from the cap vent as possible. Or just expect a drip now and then.