Dont know about Fords, but was of the opinion that some of the GM variants
came on when the ignition switch was turned on, and shut off when pressure
preset was reached.

GM also had some that activated only when oil pressure exceeded a preset
value, sometimes 3 psi. This was apparently intended to assure prelube
before
engine started.

Would like to know what you find out about the Ford.

I would replace the relay, seen this happen before with Ford relays.

I assume the Escort uses the EEC-IV ecu.

It has a LOM (Limited Output Mode) that is automatically entered if
there is a problem with the processor part. In this mode the fuel pump
runs continuously, the injectors runs a fixed duty cycle and the
ignition is run at a fixed advance, controlled by the TFI module, if
it has one.

If the processor works, then the pump is shut off after two seconds in
KOEO.

In LOM you will not be able to pull codes, as the processor is out
picking daisies, or something similarly useful, instead of controlling
your engine ;-)

So to comment on your mechanics, yes, there is a timer, but it is a
software timer that will not work of the processor doesn't work, and
no, there is no switch that shuts the pump down based on pressure, at
least not with these old systems with a return line.

I have converted a 351 Cleveland to EFI using parts from a Mustang,
with an EEC-IV, and I'm using an add on board that allows me to tune
the EEC, and one dead giveaway of processor problems is when the
fuel pump runs continuosly.

Cheers,
Thomas