vroooom ptssssh: bit confused by what your trying to do, exscuse my ignorance, but i can help you on this subject

Firstly, those 2 relays you have pictured, 1 is a XR3i/Series 2 fuel pump relay (purple one), the other, is just a 40Amp SPDT throw relay (not a fuel pump relay). Did someone tell you it was?

Also i see you say about cold starting. The auxiliary air device which contirbutes to cold start idling, is connected to the fuel pump, so basically as soon as the fuel pump starts running, the auxiliary air device heats up. So if you bypass the relay with a wire link, the fuel pump and auxiliary air device would be running well before u start the car, leave it too long and the auxiliary air device will of already closed up, making it run like a bag of nails until up to temperature?

If this isnt what u needed, or u need anymore info give me a shout (i wired my car from MK3 XR3i (series 1 equivalent) to Series 2 running gear.