If fuel is coming out of that hose, you might want to check the two hoses inside the tank that attach to the two left-hand (by left-hand, I mean from a rider's point of view, not as shown in the picture) metal spigots that pierce the tank bottom; the hose in your hand attaches to one of them. If either of the internal hoses are torn, disconnected or split, you will likely have fuel spilling out of one of the two external hoses. As you probably already know, the other two heavier duty hoses attached to the right-hand spigots on the tank bottom are the fuel injector supply and return hoses.
There are two hoses inside the tank that connect to the two left-hand spigots that you see on the bottom of the fuel tank. One internal hose goes to a nipple on the bottom of the fuel cap surround, theoretically so that any fuel that might accidentally overflow into the surround when refueling (or water from rain) has a place to drain. A hose from that external tank connection hangs down and ends behind and below the swingarm pivot (that should be the hose next to the connected hose in your hand).
A second internal hose from the other tank spigot connects to another nipple on the bottom of the tank's filler cap surround that goes to a vent right under the fuel cap, so that air can vent into the tank as it empties, avoiding a vacuum (and hopefully an imploded fuel tank). As Ritlee says, the external hose that you have in your hand normally would route forward to a plastic charcoal canister mounted on the right side of the frame near the fairing stand-off (yours appears to be missing from the pics you showed in your other thread), and that canister also has a vacuum connection going to a nipple on each intake manifold which should draw fuel vapors from the canister into the intake (there's another hose from the charcoal canister that either vents to the open air or maybe connects to the airbox, I can't remember which). Eventually, the canister may fill with liquid fuel which reportedly could cause fuel mixture issues, so it's pretty common practice to:
1) remove the canister and its hoses.
2) cap the two nipples on the intake manifolds or better yet, replace the two nipples with small sealed machine screws,-- since your canister is already MIA, make sure that whoever removed the canister didn't leave unsealed openings in your manifolds where these hoses used to connect since that could cause a lean condition.
3) join the two left-hand metal external spigots on the bottom of the tank with a Y-fitting using a couple short hose sections, and connect the 3rd leg of the Y-fitting to the existing hose that's currently connected to the 2nd spigot from the left in your picture. This configuration joins the vent and the drain hoses from the tank into a single hose which is open to the air below the frame; apparently this is the way some non-USA SSie's were set up from the factory.
All that to say that if the hose in your hand leaks, check the tank's internal plumbing

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Hope that is at least as clear as mud and didn't put you to

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Bryan