The low light is activated by a contact closed in a separate circuit when the sending unit float descends to the bottom. This simply cannot happen if the fuel in the tank is above that level. I would doubt if your problem is related to the sending unit, more likely the wiring or at the readout end.

Steve

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'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7