The ECU (KEY ON) controls the Fuel Pump Relay and NO, I don't think the short is before the relay.
Need visual inspections of the following:
Disconnect Bulkhead C100 (Engine Harness to Instrument Panel Harness).
Backside of Fuse Panel.
Both ECU connectors.
Was this vehicle ever driven underwater?
Let's define "primes my fuel pump". Too me, that means fuel pump ON for 2-3 seconds, then OFF. This primes the fuel rail with pressure. Is that what your seeing or is fuel pump just ON?
Did vehicle always have this problem? Is it something new or just discovered? Is vehicle equipped with Headlight Delay Module? Does it have a HD LP DLY fuse?
If your looking for natural wonders, Bay of Fundy in Canada (New Brunswick, Nova Scotia). I must say its a sight to see so much water move in and out of the bay daily.
The only thing I notice, on the Power Distribution page of the 88ElectManual, is each fusible link has both a color and a gauge value posted next to it.
Fuel pressure numbers seem good allowing for a little slop in the gauge. Ideally would be 39psi at KEY ON and 31psi at IDLE. Maybe time for a secondary tune up. Plugs, wires, rotor and distributor cap.
Assuming your not running fan current through the switch, your wiring seems to be correct.
NOTE: Ground coming off of the switch is solely for the Fog Lamp ON indicator. Determine if the 'ON indicator' is the source of the heat by disconnecting the ground circuit on the switch.