Weirdly, it is pretty common for twin outlet petcocks to only dispense fuel from one outlet or the other with no lines attached. Connected to the carbs, one line fills, then the other. Possibly there is nothing wrong, just cap the flowing outlet with your finger and see if fuel flows out the other. There is probably a simple explanation for this phenomenon, but I don't know what it is.
The two outlets are direct connected to the petcock bowl. Fuel flows from the tank, through the selector valve which chooses where the it gets its fuel; either from the high level through the tall pipe (the "main" tank), or from the bottom (the "reserve" tank). Either selection sends fuel directly into the bowl. The bowl fills, and fuel flows up past the screen and into passageways to the fuel outlets. The valve assembly shuts off fuel from the tank to the bowl, so if opening the tap lets fuel flow out, it is filling the bowl, and flowing out the outlet(s). The idea is that you can shut off the fuel, then remove the bowl to clean the screen and the bowl for contaminates. Otherwise you would have to empty the tank to clean the petcock bowl. The valve has no interaction in deciding which outlet fuel comes from, so that is not the problem. If the bowl fills, it will pour fuel from both outlets unless one (or both) is plugged, though for some reason once fuel starts flowing out of one, the other often seems to be ignored until resistance is offered to the one flowing.
The "cloverleaf" seal is behind the valve lever. Usually when it is bad, the fuel will not shut off, or it leaks at the lever. This is definitely not the problem, so don't needlessly take it apart.
Lastly, FWIW, if you run clear fuel lines, you likely will see they do not fill up with fuel. But you should see fuel run down the line and stop once the carb bowl fills, and see the line partially filled with fuel. This is normal, so don't worry something is wrong. As the engine uses fuel, more will flow into the lines, but there will always be air. This happens because the petcock assembly works like an upside down "p" trap like under your sink. It allows more fuel to flow only when it is depleted down the line, so it traps air at the top, sort of like your sinks "p" trap holds water at the bottom; water can keep flowing through, but the trap is always full.
