Vacuum Hose missing? Im a newbie

[WanderingSlacker]

Hello everyone, I am new to motorcycles and passed the MSC course a few weeks ago and just picked up a great 2001 GZ250 with only 350 some miles on it. I got it checked out and it passed inspection and the shop didnt find any issues with it.

I find that if I ride with the fuel line on "on" or "res" the engine will die out and it can only be ridden without issue when in "prime". Long story short after searching around here for similar issues I found that I should probably check the vacuum hose to the petcock. Low and behold it was gone. I took the fuel tank and seat off and cant for the life of me find out where the tube should be or where its located. Can anyone help? I have no experience with bikes but dont mind getting my hands dirty.

Any pictures or anything that can help? I think theres supposed to be a t joint with a hose that connects to it (from what I saw on someone elses bike) but I didnt see anything like that on mine. Any help would be appreciated!