Possible Electrical Problem, or Just Battery?
You must have power at the inertia switch for the pumps to ever run.
You need to find the EEC Power relay and the Fuel pump relay and see what is happening with them.
The power and the fuel pump relay must click when you turn on the key.
Then the fuel pump relay will drop out in one second but the power relay will remain closed as long as the key is on and the drop out when the key is turned off.
Do the relays do this?
Do you have a good body (cab not the frame) ground to the NEG (-) post of the battery?
You must have both of these grounded for the pumps to run and the engine to run.
Did you re-hook all of the fuse links to the battery side of the starter solenoid?
This is also a must.
It clicks open, the contacts open, goes to the off state, un-picks, de-energizes, or does not pass power.
To check the fuel pump relay ground pin #6 of the test connector and it should click on while it is grounded and drop out when you remove the ground. Al so the fuel pumps should run all the time it is grounded.
The test connector:

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Ford Trucks for Ford Truck Enthusiasts

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To reword it.
If the fuel pump relay does not have any power to its contacts or the contacts are bad or the wiring under the relay is bad the inertia switch will not get any power even if the contacts close in the fuel pump relay. Then everything along the fuel system to not be able to work.
Yes that is the basic idea of it.
Yes you can just stick a wire in number 6 then attach it to a ground.
This bypasses the computer (takes control away from) and the fuel pump relays contacts will remain closed (passing power through) as long as pin #6 is grounded and the key is on. The key has to be on so that the power relays (brown relay) contacts are closed to give power to the coil of the fuel pump relay.
Yes if you pass power through the fuel pump relays contacts, the inertia switch contacts, the fuel selector switch contacts the power then should be at both fuel pumps and they should run as long as the ground wire of the pumps makes its way back to the NEG (-) post of the battery.
Note that the frame pump power does not go through the selector switch contacts so it will run with a bad selector switch but the in-tank pump will not if you have the two tank system. Of course you do not have the selector switch if you have two tanks you would then have jumper in place of the switch.
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If you did not understand the way I said the above here is how for says it works:
EEC Power Relay
The EEC Power Relay supplies power to the EEC Module and EEC System-related components. When the Ignition Switch is turned to START or RUN, voltage is applied to the EEC Power Relay coil, and the Relay's contacts close.
Voltage is also applied through the EEC Power Relay contacts to the Fuel Pump Relay, the Fuel Injectors, the EEC Module, the EGR Solenoid and the Thermactor Solenoids.
Fuel Flow
The electric Fuel Pump supplies fuel under pressure to the fuel rail and the Fuel Injectors. When the Ignition Switch is in START or RUN, voltage is applied from the EEC Power Relay to the Fuel Pump Relay coil. The coil is grounded by the EEC Module, the Relay's contacts close and voltage is applied to the electric Fuel Pump.
The Inertia Switch is a safety device that cuts voltage to the electric Fuel Pump in the event of a collision. Once the Intertia Switch opens it must be reset manually.







