On my 02 GTX DI, the tube that runs along the left side of the inner hull connects to the back side of the exhaust pipe and exits the hull in a small hole under the left front bumper lip. I'm pretty sure it's a "pisser" to indicate whether water is being circulated through the exhaust. Along the right side of the hull, there is a disconnected hose that terminates into a similar hole under the right bumper lip. I believe this hose was previously attached to the battery vent. Since I am using an unvented AGM battery, this hose serves no useful purpose.
You should be able to stick your head into the hull and use a flashlight to see where that hose you're holding goes to. Tug on it a bit to see what moves. If you're really desperate to see where it goes, open up the front storage bin and pop off the plastic buttons on the fire extinguisher mount panel with a flat screwdriver and/or a door panel removal tool. That'll allow you to easily see into the front of the hull where the fuel tank sits.