If it were me, I'd keep it simple and apply 12V at the fuel pump (as AndrewWynn said initially).

Pull off the connector and figure out how to get 12V on the pins you need. That test cuts out any doubts regarding the DME, the relay, and even the wiring (which could be a problem you have not considered yet).

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2001 X5 3.0i, 203k miles, AT, owned since 2014