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The in-tank pumps (boost pumps) are used for shifting and locking the Selector Valve and priming the Fuel Reservoir and Hi-Pressure Pump. These pumps are not needed again unless you are switching tanks, run out of gas (or low on gas) or running in Mountains.
The Mechanical Selector Valve will not fail in this way, when it fails (an "O" ring sticks on its shaft from not being used) it will fill the front tank when running on the rear and will not fill the rear when running on the front.
So we have a system that has the Mechanical Selector Valve locked to run on the front tank and as long as the check valve is good in the Hi-Pressure Pump and the system is primed it will run fine just running off the Hi-Pressure Pump with both in-tank pumps not running while it takes gas from the front tank with the rear tank selected.
You need the rear pump to run and pump to unlock the Mechanical Selector Valve and switch it to the rear tank.
Your last posting with the info and the check valve was to the point and explains how the gauges switch while the truck still runs off the front tank. Looks like the rear tank comes out.
i have the exact same problem with my 1988 ford f150.it only draws fuel from the front tank.when switched to the rear tank the gauge goes all the way past full and draws fuel from the front tank.The fuel gauge when switched to the front tank stays on full for a long time then bounces around finally stopping when the tank is almost empty.The switch on the dash tests good.I think the high pressure pump keeps the truck running when switched to rear and the gauge bouncing around and not working right is a faulty flex fuel module located under the dash.The likely culprit is the rear tank fuel pump. So my next step is to drop the rear tank and check the pump.(to hard to hear with the high pressure pump whinning)