Low fuel light

My low fuel light comes on randomly at 1/3ish of a tank left. Will be off the next time I drive it or not. Any ideas what's up? '93 XJ, 4.0 AW4, 231.

mine comes on at a 1/4 tank pretty consistantly... i try and not let it get that low though.

When cornering?

So far always below a 1/2 tank, will do it when staring out first thing. Doesn't go off when you turn the key off and back on again but may not be on the next time I drive it.

Might be a failing sending unit.

Pull the sending unit, attach ohm meter and move it through its range checking for bad spots.

My 91 FSM says the sender provides variable resistance to the gauge cluster, where its used by the gauge needle and a "low fuel warning module" separately

When the module senses 66.5 ohms or less from the fuel level sender for 10 continuous seconds, the indicator will light. The indicator will remain on until the module senses 63.5 ohms or more from the fuel sender for 20 continuous seconds.

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If the gauge needle isn't jumping around, then I would assume the sender is okay and the module is bad. According to the diagrams I have here, the module is inside the gauge cluster and it looks like it's a semi-serviceable part if you want to mess with it. Might just need to clean the contacts