I found the problem today. One of the power wires to one of the fuel pumps had broken. It was hard to see because it was the one furthest in the shroud and the furthest wire in. I discovered it by disconnecting one of the wires from the pump that was visible. With the wire disconnected, the car would not start.

Thanks for all the responses.

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1988 420 SEL
1991 420 SEL with 560 motor
1993 Miata