The description sounds like a fuel pump that is starting to fail or has a crack in the delivery line inside the tank. It would let air into the line and lower the fuel pressure at the engine. Those could easily cause the issues you have. The lower fuel pressure would cause the engine to run lean and misfire which would turn the light on, then once the car levels out or you add fuel it stops getting air and it runs better. I would put a fuel pressure gauge on it and then run it some to verify that the pressure is the issue. The pressure with the key on engine off should reach about 43 psi, then with the engine idling it should be around 34 psi.
Your car doesn't have a test port so the gauge gets installed in the line between the filter and engine under the hood. If it tests low or fluctuates a lot then the pump is likely the issue. Replacing it requires that gas tank be lowered and then the pump replaced.
1. Disconnect battery ground.
2. Release fuel pressure.
3. Drain fuel into an explosion proof container.
4. Support fuel tank with jack.
5. Remove strap bolts.
6. Lower fuel tank from vehicle.
7. Unbolt fuel gauge assembly.
8. Replace fuel pump.
Reverse the process to put the tank back into place.
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Tuesday, August 25th, 2020 AT 3:19 PM