I also have a 1980 fiat spider fuel injection problem.
It starts but quickly stops. I am getting power to the pump but when I use the starter the pump will not pump fuel. I hooked the fuel pump to a battery charger and it seems to work fine.
I can't seem to locate the double relay so I haven't checked that yet.
I bought this and it cranked fine. I drove it home and now it won't start.