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I once had a similar problem in my old 88 IROC. The ground to the fuel pump relay was intermittent in turns. Ran a new ground wire, and all was fine. I diagnosed that via a scantool, watching the fuel pump voltage when the problem occurred... at least that's how I remember it happening, it was almost 10 years ago
This sounds like a short or open wire.
If you don't have a scantool hook up a volt meter via long wires from the where the fuel pump/gas gage wire bundle is, just before it goes in to the fuel tank. Drive the car to reproduce the failure and watch the meter for fluctuations.
Another thing to look for is make sure the O2 sensor wire has not shorted to exaust or exaust heat shield. I've had the sharp edge of the heat shield cut through the insulation of the O2 wire and it caused the engine to stumble and die. If this is the case just fold the extra wire up on its self and add a zip tie.
Iwasnt referring tothe ABS system, I meant the bladder in his gas tank. If it was deformed enough coudnt it uncover the FP pickup enough in a turn to quit? Im reaching here, but....
It has to be something simple....Hopefully.