Would appear this bike was only to have 2 lines from the petcock. One is a 12mm OD line the other is a bit more mysterious. The carbs have two feed lines so if the math is correct then there should be a "T" in the line from the petcock. If there is a 3rd port on the petcock and it is blocked it could be that this isn't the original petcock, in 11 years a lot can happen to a bike.
The carbs are dirty, maybe have other issues, but are for sure dirty. The big thing here is to not damage the diaphragm (#5), these are the money parts. Remove the cover (#28) very carefully, making sure that the diaphragm isn't stuck to the cover. Remember it's 11 year old rubber. You will need new bowl gaskets (#13) and o-rings (maybe). Don't freak about the o-rings, there's Grainger in Lexington at 1351 Georgetown Rd., Lexington, KY 40511
Phone: (859) 252-2302 Branch Hours: 7:30 AM - 5:00 PM (Monday - Friday)
They have metric o-ring kits in various durometers but go with the 70 durometer buna. The viton might work but viton tends to have an uncontrollable shrink rate when molded so they tend to be on the low side of the size tolerance. here is a link to metric o-ring page:
http://www.grainger.com/Grainger/wwg/productIndex.shtml?operator=prodIndexRefinementSearch&originalValue=metric+o-rings&L1=Seals%2C
I'd drain the carbs into a some clean container that I could see what is in the bowl. To do this put some tubing on the drain outlet on the bottom of the carb bowl, turn the drain screw (#18). You can use aquarium tubing for this if that is all you have. (note: cold engine when doing this!) Look for rust, if you see rust then you need to address the tank or no amount of carb parts or seals is going to help for long if at all.
Good luck and don't feel rushed or force anything, come here and ask first, these guys are a pretty good bunch to have advise you through this process.
Take photos from all angles before breaking the rack down, work taking it down so you can pull one carb off and take this one apart by itself. Clean and rebuild it before starting the next one. Doing it this way gives you a reference if you forget where something went or in what order plus you don't mix like parts from carb to carb and keep them in order to go back into the rack the same way they were.