1986 300E

Has this happened to you?
Fuel light just came on. Tank is low, but several gallons remain.
Take an exit ramp (long sweeping right turn).
Hit the throttle to merge onto highway, and... nothing.
Sputter, sputter.
Almost get rear-ended, 3-4 seconds pass, power kicks back in, and no problem...

Is it just me, or is this common?

Of course the fuel flows 'to the right' to get to the pump, but why would it go dry with 3+ gallons remaining?
Given enough fuel, this does not happen.
I have no other symptoms of a fuel problem, though I confess to having a cheesy "Made in Taiwan" pump.

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1986 300E 5-Speed 240k mi.