I had this problem with my car. I had a spare relay that I swapped in and it started right up. I took the old relay cover off and found one of the pins in the middle of the circuit board was burned. It must have compromised the solder joint. I will be re-soldering the pin and then retesting since I read that others have done this with some success. Evidently, if too much current goes through the relay, the pin solder can melt. If it becomes chronic, then the fuel pump(s) could be bad.

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VR
1967 250SL