Download the 1987 Fuel and Emissions book from the service manuals link in my signature. You'll find the following wiring diagram in the bottom half of PDF page 123

The ECM drives the fuel pump relay for 2 seconds when the ignition is switched to RUN and continuously when the key is turned to START.
Once the Oil pressure comes up to 4PSI the Oil Pressure Switch, this is not the gauge sender, supplies power to the fuel pump circuit as well. It's a backup for the fuel pump relay. I believe this switch is on the block near the oil filter.
If you have dual tanks the TAN/WHITE wire feeds juice to the tank switch to select the LH or RH fuel pump rather than directly powering the fuel pump.
The Fuel Module is usually only used on the 7.4L 454 but the service manual claims it was sometimes used on the 20 & 30 series trucks with the 5.7L 350. This is sometimes called the Hot Fuel Module. It's supposed to power the fuel pump for 20 seconds when the ignition is switched on. This is on IGNITION power.
The ECM B fuse is on direct battery power not switched. If the fuel pump relay or the Oil Pressure Switch are malfunctioning the fuel pump could run with the ignition switched off. .
First. Put a good charge on the battery with the Ground unplugged. The ECM doesn't like low voltage and it may be malfunctioning because it doesn't have enough juice.
Unplug the fuel pump relay when the pump is running with the ignition OFF. If it shuts off replace the relay. If it stays on unplug the oil pressure switch. If that fixes it replace the switch.