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You may have a weak fuel pump that bleeds the fuel backwards after a while of sitting. One of my trucks does the same thing.
Or the plugs on the bottom of the carb may be leaking.....
The Q-jet carb bowl only holds a small amount of gas. The gas evaporates in a few days so you have to fill the bowl again. I recommend crank it for 1-2 seconds and the fuel pump makes a stroke and the gas will start to flow. Let it sit for 5 seconds and then crank for 1-2 seconds(save the battery & starter) About 3 or 4 times you can pump it and it'll start if the fuel pump is OK and the accelerator pump is OK. The fuel pump can be OK but If the choke doesn't close and the accelerator pump doesn't work it may not start without pouring gas in the carb.
Quad should fill up and start within 15 seconds or so with a good fuel pump.Possible your needle is sticking when the bowl is dry.I tried the suggestions on how to get it to start and it didn't work so I will take a look in the carb, I have work on motorcycle carbs but never autos so this should be interesting.Once I get this pickup started man it just purrs and starts with easy as long as I don't let it go for more than a couple days.The pickup came off a huge ranch in southern New Mexico and is totally and I mean totally rust free, all the bolts came off so easy.
R U putting fuel down the barrels of the carb or in the float bowl when it starts.