I removed the "T" and then hooked up a vacuum pump. One carb was dripping fuel and the other was dry in the filter and the carb. New filters and New fuel line.
Sounds like a stuck float on the leaky carb, depending where the fuel was coming from.
On the other side, maybe the one port on the petcock is clogged with rust/debris? Take it apart, check/clean? That's the only reason I can think of for one side flowing and the other being dry.