A reducer, IINM, is a heavier duty resistor that will reduce the voltage from 12v to 6v.
One would have to be installed before the fuel gauge for it to read correctly, as the gauge is basically voltage meter that has a top end at 6 or 7v.
If you feed it 12v, it certainly won't read correctly, and may burn up.
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Yes, a dropping resistor gets hot. It's supposed to. That's the way resistors work. They convert the excess electricity to heat.
