The stock Harley petcock that's vacuum operated, if not modified, has a spring and diaphragm inside that cuts all fuel from flowing through it regardless of whether it's on "run" or "reserve".
The only difference between run and reserve is which hole the fuel comes down from the tank. If you pull the petcock and filter screen, remove the filter screen there's two holes, one of which has a tube coming up. That side with the tube is the "run" side, the side without the tube is the "reserve" side. The petcock valve has an offset hole so that the hole is in alignment with one side or the other, that's why "run" and "reserve" are 180° from each other. Either way, to get to that valve, gas has to get through the diaphragm.
As to the carburetor, the Harley/Keihin CV carb, the accelerator pump doesn't just run or go. If you have fuel in the carb and float bowl, when you twist the throttle from 0 to open the throttle plate, a piece of metal pushes in against a diaphragm to squirt fuel through the accelerator pump jet. Even if the accel pump isn't functioning, the bike should still run as long as fuel is getting to the carb (you'll just have piss poor acceleration).
Now, the float bowl has to be getting gas to it for the accelerator pump to get gas. If the carb bowl is empty or near empty, there's no gas to refill the accelerator pump for it to function. If your carb was completely empty, but has been refilled, you might have to blip the throttle once or twice to prime the accel pump before it squirts. If fuel isn't getting to the pump, it's because it either isn't getting to the bowl or is clogged. If gas is getting to the accelerator pump and it isn't pumping, the accel diaphragm is bad.
So, check your fuel filter screen. If it's clogged up bad, that'll be an issue. The petcock is a pretty simple thing, if there's nothing clogging the valve hole inside and the diaphragm is good, then the issue isn't the petcock. If the diaphragm fails, all that will happen is gas will leak at the petcock (once the carb is full, the float stops more gas from entering the carb, assuming all of that is functioning correctly). As long as the petcock isn't clogged, that isn't going to be the issue. Other than clogging, failures there will result in gas leaking, not stopping.
You said you overhauled the carb. OK is the carb bowl not getting any gas at all? One other possible issue is the float bowl and float needle. You didn't accidentally bump or mash the float, did you (bending the float tab resulting in the float needle remaining closed or becoming damaged)?
As Schmidty said though, check that whole vacuum line. It's fully pressed onto the back of the carb, right?
The line should go from the vacuum fitting on the back carburetor to a T piece where one side goes to the VOES and the other to the petcock, generally speaking.