I would check the accelerator pump, this will be a diaphragm on the #2 carbie. when you goose the throttle a fine spray should come out of the nozzles in the carb throats. This is to overcome the lean running of the carbs as per the EPA.
Thanks for this, I'm unfamiliar with accelerator pumps but I will look into how to inspect them.
I don’t know the CV carbs that well, but I believe there should be two hoses going to the petcock. One for fuel and one for vacuum. That nipple that’s open is a vacuum line and should have a hose going on it either to the accelerator pump or to the petcock. Post some more clear pictures of the carb rack and petcock. I’m thinking it’s just an issue of not having all the right parts for the carbs installed.
I was told the outlet was an overflow tube and should have a line running from it to the ground in the swingarm area? There seems to be a little ring on the side of the carbs that looks like a small overflow fuel line should run through it as seen here in the red circle:

There's nothing on the underside of the tank or the petcock, it looks very simple. here's an overhead of the left side of the carb rack. The hose in the green circle runs to the underside of the outlet where the fuel was coming from (green circle in other picture) and the hose in orange connects the 1&2 carbs and runs over to the 3&4 carbs (orange circle in other picture). The orange line also connect back to the air box via a T connection I believe.

And yeah, regarding the video: since it has an accelerator pump then running the bike without the tank installed and no vacuum line going to the petcock you won’t have proper fuel flow. What’s your fuel source when the tank is off?
I was running it with the tank sitting beside the bike with a longer piece of fuel line. Like I said, I don't see any thing for an additional fuel line to connect to the fuel tank or petcock.
Thanks for the help guys!