How does the vacuum work on the petcock suzuki vinson 500?

The petcocks are vacuum operated petcocks. This means that they have a little diaphragm and valve set-up in them which responds to engine vacuum and allows fuel to flow only when the engine is running and supplying vacuum. This is is how things work when the petcock lever is set to the "on" or "run" setting. So we see that the "on" setting is actually the "off" setting when the engine is not running. So if the engine quits for any reason (as in a "down" situation), the petcock(s) will automatically close and prevent the fuel from flowing out.

These petcocks also have two other lever settings:

The "prime" setting bypasses the vacuum function and allows fuel to flow at all times, even when the engine is stopped. The purpose of this setting is to allow the carb float bowls to be filled when the engine is not running. Note that if you run your petcock(s) on the prime setting all the time, you lose the safety feature provided by the vacuum petcock. Note also that on this setting, fuel is prevented from flowing out through the carbs, into cylinders, etc.) only by the float valves in the carbs, which close when the carbs are full. Should one of these float valves stick open or leak, you then get flooding through that carb.

The "reserve" setting is used to access an additional amount of fuel when you start to run out. Here is how this works. These petcocks have inlet towers which stick up into the tank. In the "on" position, fuel flows down to the petcock through an opening high on the tower. So when you "run out of fuel" you actually have some more fuel sitting in the bottom of the tank which lies below this high inlet. When you turn the petcock lever to "reserve", a lower inlet near the bottom of the tower opens, so you can gain access to this last bit of fuel in your tank.