The fuel level gauge operation has nothing to do with the primary fuel pump running.
The -13&P schematic does show the batteries, starter motor and everything else.
The primary fuel pump is to the right of the engine. The Aux fuel pump is behind the engine.
I'd suggest putting S1 in the Run position and then using a meter measure the DC voltage at the connector to the Primary Fuel Pump with respect to chassis ground with the pump connected. If both readings are 0 volts then you're losing 24 volts somewhere from S1-4 to the positive lead to the fuel pump.
If both readings are around 24 volts then the ground connection to the fuel pump is open.
Be sure diode CR2 is in place and not blown.
Be sure CB1 isn't tripped.
Be sure the Emergency Off button is pulled out.