No fuel pump

What is it that causes the gas to squirt through the pilot jet if there is no fuel pump?

Fuel pressure/ Vacuum

What I'm asking is, what are the parts of the fuel pressure/vacuum system that results in pressure in the bowls that squirts fuel through the pilot jet? I don't believe that fuel is coming out of the pilot even though all the passages are open, because if I open the throttle and squirt starting fluid down each carb I can get a couple of revs out of it before it dies.

Sounds to me like your carb boots to the head are leaking. try checking the screws and clamps to the carbs and head. Or they might just be old and have cracks in them. If they don't suck hard enough you won't get any fuel.

Yes, check the rubber boots between the carbs and the head like dshelly recommended.

My understanding is as follows: There are small holes in the throttle bore that are very near to the throttle plate when at idle position. With the throttle plate just barely open, a high velocity of air passes these holes. This creates a vacuum that draws fuel through the pilot jets.

Unless your idle setting is completely closed, I imagine that your problem is NOT a lack of vacuum, but rather a stopping up of the pilot jets. They are so small in size that any tiny particle of dirt, tank sediment or varnish from old fuel can and will stop them up. Also the passages that lead to and from these jets must be very clean, otherwise material will stop them up in a short time. Clean, clean and clean the carbs, and use a good filter in line. Good luck.

what allows fuel to travel up the pilot circuit is pressure differential the float bowl is vented to the atmosphere (high pressure) and the carb throat has a vacuam (low pressure)in it from the suction of the pistons so as long as the vents arent blocked off or pilot circuits themselves aren't plugged up then fuel should rise up into the carb venturi. sounds like something is plugged still.