64 Dart 273 Engine Vacuum

If the engine runs for 20 seconds, with the throttle at a more or less a normal position, then I would NOT suspect a jumped chain.
I would suspect,
1) a non-vented fuel-tank, or
2) a perforated jumper hose, probably at the back, between the sending unit and the main supply line.. When this happens ;
when the tank is full everything can be working fine, as the pump pulls enough fuel for the engine to run on, during normal operation. The fuel does not leak out because the jumper is higher than than the fuel in the tank.
But as the liquid level in the tank drops, the pump starts drawing more and more air from the leaky jumper. Eventually the engine quits for lack of fuel in the bowl.
After it shuts down, the fuel that remains in the line migrates to the lowest spot, which is usually the pump. Then with a long crank-time, the bowl fills up and the engine begins to run. The pump continues to move the fuel up to the carb, but when it runs out, the engine quits again. But this time, the line from the pump to the tank is completely dry, so it will not start a second time.
The Proof of this is that with the tank full the engine returns to normal.
Now, that jumper can be brand new and if screw clamps were used, it will still do this. What can happen is if the screw-clamps are over-tightened, the fuel-line will bunch up under the screw head, and introduce a pathway for air to get sucked into the line. So whenever screw-clamps are used, two are needed with the heads offset by 180 degrees to eliminate the pathway.... and this needs to be done on BOTH ends of every jumper.

Now, if the front jumper is the culprit, the same thing happens, EXCEPT:
After the engine quits, air in the line will migrate to the highest spots, which are, 1) from the pump downwards to the hard supply-line, and 2) back at the rear jumper. Assuming the rear jumper is Ok, that line will be under vacuum for a few minutes, and while the air is traveling to the rear, fuel may be syphoning back towards the fuel pump. After the Vacuum relaxes, the line can be full of fuel almost all the way to the pump. The jumper at the pump, if faulty, usually seeps a bit, but the underhood heat may evaporate it faster than you can spot it. But you can smell it, and it will stink up a closed garage.
So now, with line full of fuel, with a bit of cranking, it will start up again! And it will run until the vacuum in the line can no longer pick up the fuel, or the line is again full of air.
To prove that this is happening, you start with a tank full of fuel, and the fuel bowl at the carb, full, then remove the supply-line from the pressure side of the pump and re-route it over to a clear glass mason jar of at least 1 quart capacity, secured to the car, as high up as possible; I use a 2liter pickle jar, hung from the open hood. Next I pressurize the tank just enough to prime the line, being careful not to blow up the tank. When no more bubbles come out the line, then it is primed. Then I return that fuel to the tank. With the jar once again empty, I anchor the supply line to the bottom of the jar, so it cannot flip out, and Finally, I start the engine. It should idle for long enough to complete the coming test. You need a helper. One of you will idle her for exactly 20 seconds, then shut it off. The other one will make sure the hose stays in the jar, does not overfill it, AND very importantly, watches for the cessation of bubbles.
The only air in the line before you started the engine, was whatever got into it when you plunged the supply line into the jar, so a few inches worth. Therefore, you can expect the pump to blow that outta there in a couple of seconds, and after that, only liquid gas should come out.
If the bubbles never stop, there is your proof, that the pump is sucking air.
Also, the pump must be able to pump about 1 qt per minute, IIRC, so in 20 seconds that comes to ~11 ounces at idle.
Let me say one more thing; at idle and parked, your engine cares not even the slightest what pressure the pump can put out. It only cares that the float-bowl stays at a specific WET level.
Pressure is only required to move a sufficient quantity of fuel under acceleration, at or near full-load.