Welcome to Ninjette.org, Domenic !!!
It could be related to the fuel feeding system.
The tank must be ventilated through the cap, which get clogged as years go by.
Then, you have interior mesh filters inside tank and another by the end of the fuel hose.
The petcock is vacuum activated; some leaks in the vacuum hose and no fuel flows down.
There are two float valves inside the carbs that should keep certain level of fuel inside the bowls, but again, those tend to go bad with the years, either leaking or getting stuck in the closed position.