The fuel pump relay controls more than just the fuel pump.

It will shut off power to the fuel pumps if it doesn't recieve an RPM input for more than a second from the electronic ignition control unit. If there's no output from the ignition control unit, that probably means no spark, so a (jumpered) running pump doesn't mean anything, other than the pump probably works.

The FP also controls the cold start injector.

It's why there's so many pins on it...

Personally, I think "fuel delivery module" would be a better description of what it does; a "regular" fuel pump relay only has 4 pins; 2 for the coil and 2 for the contacts that needs to be made to power the pump.

If it were me, I'd be looking at the ignition system, especially since you've somewhat verified that the fuel pump works.

You can either take it to an indy who has all the tools (scopes, etc) to correcly diagnose it and replace the correct part, or you can risk it and break out the parts shotgun and start blastin'.

I will say, though, when it comes to DIY'ers, it has been my experience that an hour of quality diagnostic time with quality tools would have saved those people hundreds of dollars in "this might be it" parts...

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A.S.E Tech A1,A6,A7,A8 & MVAC 609 + EPA 608

Unless stated otherwise, any question I ask is about my greymarket 1985 380SEL.