There are two separate circuits in the tank sending unit. One is a variable resistor. it runs the gauge. The other is a simple switch. It controls the light.

Old sending units usually fail in the way you describe; with the bottom 1/4 tank being either not recorded or the needle bouncing through this area.

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Steve Brotherton
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician