Hmmm.. run 'til light on would not be possible with switched lines, unless you have a defective float/sensor as well.

Maybe you're getting a fuel tank vacuum happening with temperature flux, that is pulling fuel back along both lines. Creating a dry start.

Loosen the fill lid, get a whoosh (suck) sound?

You're tank vent could be plugged.

You can add a check-valve up front on the supply hose for about $10, that prevents pull back / drain back.

Tighten all the fuel hoses a crank or two on the clamps under the hood.

Maybe you're just sucking air, on a loose re-fit of some hose.

Or fuel restricted: replace filters, and make sure the main filter is not leaking / has a good seal. It could be sucking air there.

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Cheers!
Scott McPhee

1987 300D