If you can, measure the voltage across the resistor during start, you should see it go to 0V when the relay is closed across it. Then, it should go to maybe 6 or 8 volts (I guess) when the current is flowing through the resistor once the contacts open. If your contacts are fried, it may not go to 0V, and it won't hit your pump with full voltage when the ECU asks for it. And your engine will stumble...
My bet is that the relay is bad. Resistive contacts are common with age.
My bet is that the relay is bad. Resistive contacts are common with age.