No fuel to the pump

I would suggest running a short hose from the inlet port on the pump to a small can of gas, then crank the engine and watch if gas comes out the outlet port. It sounds like you checked everything else already. While it is not common, the eccentric on the camshaft could be worn down so it is not stroking the pump's lever.

You might also try sticking a tiny glob of grease on the end of the pump's lever. Install it carefully, rotate the crankshaft a few times with the starter or by hand. Remove the pump, then look if the grease has been rubbed off. If there is still some on the lever, the eccentric is worn down.

Also, double check that you have the right pump. On some, the lever is just a few inches long. Yours is really long, as in a good six or seven inches.

Loosen the line at the carburetor to see if any fuel comes out there.

I have had trouble with this on my 1980 Volare since it was new. I purposely ran it out of gas multiple times to check the fuel mileage, and found the pump will not pull a prime from the gas tank when it is pumping at cranking speed. I have to dump a little down the carburetor, then the engine will run at high idle speed long enough for the pump to start working. Once it catches a prime, it continues to work fine. You might need to do that too to see if the pump works better at higher speeds.

Also consider connecting a vacuum gauge to the inlet port on the pump. If the lever on the pump is being stroked by the lobe on the camshaft, you will see some vacuum being developed.

The bowl should be almost full. Higher level results in a slightly richer mixture, and a level that is too low will result in a lean mixture.

When air goes through the "venturi", which is a slightly narrowed area right below the choke blade, that creates a vacuum that pulls gas from the bowl, through a passage, then up to a port higher than the fuel level. If that port was lower, gas would run into the intake manifold all the time until the level dropped in the bowl. It is common for the volume of gas to be too small to see the fuel spraying in while the engine is running.

When you move the accelerator pedal and open the throttle blade a little or a lot, air flow increases instantly, but due to the mass of the fuel, it takes considerable time to get the volume to increase to the point the flow is correct to maintain the desired mixture. That causes a really horrendous stumble or hesitation. It is even possible the engine will stall if the throttle is opened too quickly. To address that lag in fuel delivery, every carburetor has an "accelerator pump". That is most commonly a spring-loaded rubber diaphragm that is moved through a linkage connected to the throttle blade, and forces a pile of extra gas into the intake manifold rather than waiting impatiently for the momentum of the gas to increase on its own. That accelerator pump insures there is always enough gas going in to match the volume of air that is going in. That is also what creates the squirt of gas you see when looking down into the carburetor when working the throttle by hand. Pressing the accelerator pedal allows the spring-loaded choke blade to close if the engine is cold enough, and the accelerator pump provides a squirt of fuel to help in starting a cold engine.

Two barrel carburetors will still have a single accelerator pump, but two nozzles where you will see two squirts of fuel spraying in. Four barrel carburetors do not need or use an accelerator pump for the secondary barrels. By the time those open up, the air volume is so high, it pulls the fuel in too quickly to have a noticeable lag or hesitation.

As a point of interest, liquid gas will not burn. In fact, if you throw a burning match into a pan of gas, the liquid gas will put the flame out as long as wind has blown the vapor away. It is critical in an engine that the liquid gas vaporizes before it gets into the cylinders, otherwise it will not burn there either to make power. The intake runners are long enough to give the flowing gas time to vaporize, and to help that take place, there are a number of methods used to heat the base of the carburetor and the incoming air. On most Fords you'll see a metal or paper tube going from the metal shield around an exhaust manifold up to a port on the bottom of the air filter housing's snorkel. That brings in air that has been warmed to help the gas vaporize. A small metal tube runs through an exhaust manifold, then air drawn through it goes through the round black thermostatic spring housing for the automatic choke. (It was real common for that metal pipe to rust, then the air didn't get heated and the choke would stay closed too long. There were repair kits for that years ago). On GM's and Chrysler's, hot exhaust gas from the passenger side of the engine gets blocked when the engine is cold and is forced to go through a passage in the intake manifold, under the base of the carburetor to warm the incoming air/fuel.

The choke helps with driveability too when the engine is cold, but in a different way. By partially blocking air flow, intake manifold vacuum tugs much harder on the gas to pull in much more of it in hopes a high enough percentage will turn to vapor and burn in the cylinders. All the rest that is still a liquid contributes nothing to producing power, and it finally becomes a vapor by the time it gets to the exhaust manifold. All of that gas is wasted and contributes to air pollution. To reduce that, the engine should be warmed up as quickly as possible.

For another comment of great value, as you drive down the rough road and your foot is bouncing and vibrating on the accelerator pedal, you are constantly twitching the accelerator pump and you are pushing in tiny amounts of extra, unneeded fuel, which is wasted. That does not happen when you are using the cruise control, so you will see slightly better fuel mileage.

Also be aware, so you can share this wondrous knowledge with your friends and neighbors, if you have any, that fuel injection adjusts the fuel/air mixture based on dozens of things the engine computer is watching. Carburetors can only be tweaked to provide the perfect mixture at idle and at some point around mid throttle. At any amount of throttle opening, if the mixture falls just slightly lean, you will notice a stumble or hesitation, so that can't be allowed to happen. On the other hand, if the mixture goes slightly rich, (not to the point of causing running problems), that extra gas goes out the tail pipe, wasted, without you noticing it. To insure the engine runs smoothly at any speed other than idle and that mid-throttle point, the engineers had to design their carburetors to be a little rich to insure that lean stumble never occurred. That means there is always just a fuzz extra, unneeded gas be wasted. That unburned gas is what causes carbon monoxide, which is much less of a problem now with fuel injection.

With older fuel injection systems that used a throttle body in place of the carburetor, the fuel being sprayed in had the entire length of the intake runners to turn to vapor. Those systems typically ran under about ten to fourteen pounds of fuel pressure. Just about every engine I can think of for the last fifteen to twenty years uses a separate injector for each cylinder, and they sit in the intake manifold very close to the intake valves. With such a short distance for the fuel to vaporize, the engineers found that occurs more efficiently when starting with higher fuel pressure. That's why it is common now to see systems running between about forty five to sixty pounds of fuel pressure.

So now you know as much as I do about carburetors. If I overlooked something, ask away.