Sorry, Becca... my bad, yours is the older type petcock.
This is also a Kawasaki thing poppy. Kawasaki (and maybe others now but I've only seen in on Kaw's) use a vacuum operated valve to stop fuel to carbs. If the engine is off, the switch is off. So you have these three choices - 1. "on" for normal service 2. "res" for when run out the main quantity 3. "Pri" to primer the carbs when they are bone dry. Pri is really a vacuum switch by-pass.
Most other bike I have seen have 1. "on" for normal operation 2. "off" when not running the engine 3. "res" when you run out the main supply.
The only other case I've seen is on FI bike, there is no fuel shut-off.
Funny story about when I bought my ZRX. I brought it home from the dealer and wanted to have a look at the top of the engine. This required removing the fuel tank. After putting it back together I didn't notice I missed the vacuum line on the gas tank. I called the dealer crying about my new bike and they were going to pick it up with a flatbed. When I went back out, I looked more careful and noticed what I missed. I almost killed the battery trying to start the bike without any fuel supply.
Anyway, I'm sure this has nothing to do with the original question. I apologize for the hijack.