Found this thread while looking for a similar issue and decided not to make a new one. Maybe I can get help here?
My f2 is a 1993 but has had a fuel leak ever since I got it. When I (finally) decided to fix the issue and when reading the Haynes manual found the there should be a Breather hose and a Drain hose that I should disconnect in order to remove the fuel tank. Now I didn't notice this until I was re-installing it but, the fuel tank didn't have either of those two connected to the small pipes (circled on the left). And I couldn't seem to find those hoses lying around either. I thought the fuel leak was going to be that sealant-like paste that the previous owner had left around the fuel tap (circled on the right) but now I'm not sure. Any help is appreciated!

 

Have you verified that the fuel is definitely leaking from the tank, or could it be from the petcock or float bowls (due to a stuck float or bad seal)?

As far as your missing hoses are concerned, you can just buy a couple of feet in length, of each hose size, connect them at the tank, and when you go to put the tank back on, you'll see the little bracket that has a "holder" for each hose - pop the hoses into their respective "holders", and as you lower the tank completely in position, be sure that neither of those hoses gets kinked (you could spray a little WD-40 around and above where they pop into the bracket, so they'll slide down easily).
Once you have the tank already down, just trim off those hoses appropriately, at the bottom of the frame.

Now, about your leak... does this only happen each time you fill the tank, and maybe persists for a little bit, then goes away?
The reason I ask, is that one of your missing hoses is an "overflow" hose, which is meant to safely route fuel to the ground, in the event you fill the tank too high - if you look around the filler area, with the gas cap open, you'll see the hole, which leads eventually to where one of the missing hoses should be.

 

hmm well I see what you mean that it's only supposed to rout extra fuel down so I'll need to add some fuel hoses in there. So just to make sure, those two pipes which I circled on the left just go down to the bottom of the frame? They don't go anywhere?
But in regards to that leak I can find a pattern to it. I've been keeping an eye out for it and sometimes over night after I've ridden for a while it'll smear my cover so I know it leaks after using it. Other times, when I'm starting it the leak starts up for a while and then stops.
I took it to Southbay Motorsports here in San Diego and a guy took a quick look at it and immediately decided that the issue had to be the Float Valves and said that I should buy all 4 of them and replace them right away.
._.

 

Ah! And when I took off the gas tank I saw what you mean by the overflow of the fuel but I'm pretty sure the fuel tap was leaking too.....unless I didn't see it right??
I'm not sure but thanks for the advice--I'll probably put the new hoses in today.
Oh BTW I did find a little crack on the side of the Fuel Tap. You can faintly see it in the image. It's where the black plastic meets the metal (inside the right circle)

 

That is correct, the hoses don't connect to anything else - you just need to route the overflow hose to where you would want excess fuel to flow.

It sounds like the guy you talked to is just trying to make a sale - most likely if the fuel is leaking from around the carbs, a stuck float would be the suspect, but cleaning and examining them would be the thing to do, not buy new ones before they've even been looked at - unless I'm missing something here, if I were you, that would be my last visit to that shop, or at least, I would not deal with that particular guy anymore.

 

Alright so cleaning and examining the float valves and making sure those hoses route any excess fuel correctly? Got it. Today's a decent day to take my bike apart anyways.
Yea that guys didn't seem to take much interest in the actual problem. Besides it was like $400+ for the float valves and $300+ for the labor! Unfortunately that's one of the only places nearby that's dealing with motorcycles. They practically monopolized the damn place. Everywhere else is either too far or too shady...heheh
Thanks a lot for the advice JNS!

 

Oh quick question...a buddy of mine says there's a spring in the fuel petcock that only allows passage of gasoline when the bike asks for it. He said stretching that spring or replacing it with one that provides more pressure fixed his problem a couple of years back but on a completely different bike; you think I should take apart that to check it out. He showed me how it works and everything but if I damage it, the piece is around $165 and I'm not sure if it's worth the risk...?
Thanks again for the help.

 

OK, so upon replacing some of the older hoses that ran from the gas tank to the bike I found that several of them were in fact kind of cracked around the edges and decided to replace the ones that are like that. Which is more than I had hoped. One of them was even missing a bracket-like pin that holds it in place (although that didn't seem to affect anything in particular in regards to the leak).
But I did catch the Petcock leaking red handed. But not from where I thought...it was near the handle *and* where the insides are; so I'll probably end up replacing the whole thing if I can't fix the issue--but since I didn't get around to checking and cleaning the Float Valve I'll decide afterwards.

 

OK, without a doubt DON'T go there again! Those float valves are only $18 each!!

 

If it acutally is an F2 petcock, it is actuated by vacuum from the engine.

You can test the petcock easily enough: just run some fuel hose from the petcock to a gas can, and with the petcock in on or reserve, some fuel in the bowls so you can start the bike, and the vacuum line from the petcock connected to the motor, start the bike, and the vacuum should open a diaphragm, so fuel can flow - shut off the motor, and disconnect the vacuum line - the fuel should stop flowing immediately.

Now, if fuel starts flowing in the "On" position, before you apply vacumm by running the engine, then it's shot, and of course, if there's no vacuum connection on the petcock, it's not an F2 petcock.