[alantf]

I noticed that you said that the petcock was in the off position. There is no "off" position on the GZ petcock, so unless it's been swapped for some reason, the stock petcock has three positions. Run, Prime, Reserve. In run, engine vacuum opens the petcock, and shuts when the engine is switched off. (so you leave it in run, all the time) Prime lets fuel flow freely to the carb, so should only be used when starting a bike with a dry carb (then switched to run when the bike is running) reserve pulls fuel into a pipe that is shorter than run/prime, so lets you know when you need to fill up quickly.

You say that the carb is clean, but the carb is the achilles heel of the GZ, so you, at least, need to run carb cleaner (mixed into the fuel tank) every 3 or 4 tankfulls.