It sounds like you're on the right track with the fuel pump relay or ECM. There might also be a fuel pump control unit ('fuel cut unit') as well. Loyales had them, but I'm not positive about the GL wagons. Here's the wiring diagram from the Subaru manual:
The fuel pump relay (on a Loyale at least) is under the driver's side dash to the left (I think) of the steering column. It is a cylindrical metal relay and should be next to a square brown relay (ignition relay). It gets power from fuse 11 (which is good on your car since the fuel pump runs with the check connector) and signal ground from the fuel cut unit.
I about pulled my hair out trying to find a wiring diagram for the fuel cut unit, but didn't have any luck. Basically the fuel cut unit gets a tach signal (yellow or yellow/green wire) from the distributor, a key-on power signal (or key-on ground from the ECM? I can't remember which, but that would make more sense), a constant power source, and a hot-in-start signal (black/red wire) from the ignition switch. From these signals, it will run the pump for a few seconds when you first turn the key on (from the key-on power signal/key-on ground), then stops until it sees the hot-in-start signal and then a tach signal indicating the engine is running.
The fuel cut unit is a blue box about 2"x3"x1.5" with a 6-wire plug going into the side of it. It's up under the dash near the fuel pump relay if I remember right.
Hopefully that is enough info to begin your diagnostics. There is a test procedure for the fuel cut unit which basically tells you to check each wire for the appropriate signal. I can dig it up if you need me to.