The petcock is vacuum actuated.
If you look, there should be a small vacuum hose on the backside that runs down to carb 1. There is a hidden prime feature that you can use: undo the phillips head screw on the front side and rotate the knob past, fuel should flow. Also, you can check the vacuum portion by applying suction to the vacuum hose, fuel should flow. There should be no gas in the vacuum hose.
The bike is also only going to use as much fuel as it needs, basically, it will only flow till the floats stop the flow into the bowls (that is, as long as the floats aren't clogged and hanging open). So once those fill up, it won't take any more till needed.
Even when the bike is running, all I ever see is a trickle through the fuel hose/filter. I'm sure at higher revs the demand is higher but at idle not so much.