No, not from my Windstar manual - that was sold many years ago on eBay after the Windstar met an early death.
I was looking at a wiring diagram for a 98-02 Crown Vic online somewhere (see below for a different example, but showing the same as what i remember). It is possible everything I wrote is incorrect, but unlikely. I think more likely I mis-interpreted the "Fuel Pump Prime Connector" purpose: It is not a bypass, but a way for the service technician to bypass the relay and prime the pump.
The Circuit numbers (87, 86, 85, 30) are standard nomenclature for the industry: 85 & 86 are coil, 30 is 'common', 87 is NO and 87A NC contacts.
I speculate that the fuel pressure is regulated in the fuel rail, mechanically. Often hard to get at or see, but look for the fuel rail, and a cylindrical hat-like object at/near one end. (I come to this conclusion based on their use of a mechanical relay: Hard on the relay contacts to try to do PWM pressure regulation that way).
I'm in the car industry, this matches how my company does fuel pumps, so it seems somewhat 'typical'.
==============
OK, we get power OUT of the relay, and this makes the pump run audibly. (Can't hear for sure with the engine running, but let's assume it does since 'prime' works OK).
This points to inadequate fuel volume delivery. This can be a bad (worn) pump, clogged pump input, clogged line from pump to fuel rail. Can't think of anything else it could be, based on what works so far.
Still have the old fuel filter? Cut it open and see if it's filthy or not. A positive answer helps condemn the pump, a negative answer doesn't help much at all. Some spoo in there is normal.
The service manual should have a pump delivery test. There usually is a service connector on the fuel rail, where you connect a hose and then run the pump for x seconds, measuring the volume of fuel it pumped. All the usual precautions apply; the hose helps make this safer but not entirely.
You use the "Fuel Pump Prime Connector" to run the pump (likely easier to get at than the relay). This is how I emptied the Windstar's fuel tank before I sold it for scrap (but I bridged the relay). Got out nearly 10 gallons, a significant fraction of the vehicle's value at the time.
