awg

gauge shows empty, low light on, I know the '96 has a weird arrangement with sender, pump and regulator part of an overall assembly

thought I should start by checking at the external plug, but I cant quite figure what I should be looking for, even with the attached circuit diagram

should I be looking for path to earth via those 2 x DB wires? (3) & (5),,, that path may now be broken if the sender is faulty?

I had the unit out a couple of years ago, and replaced the pump, sock, and o-ring...those parts were faulty when I bought it

gat

Just 3 to the cluster shows the level. A variable resistor is used on a float to yeild the level of a tank. I'd fill the tank whole watching the gauge with the key in the on position. If at any point or points or range or ranges it shows level, then drops I'd suspect the resistor in the fuel pump assembly. If there is no good point nor range, then I'd suspect an open between the the connector to the fuel pump assembly and the cluster. It could be the cluster as well. If you are testing for resistivity between the sending unit (3) and the cluster, then you are already in position to test the cluster. You'll have to pull the dash apart to test that.
If the filling pump test fails, then I'd have a spool of black wire and a new gauge ready to install and return whichever that you don't need.

awg

as the truck is my spare & unreg, cant really fill the tank to observe, not essential, but still wish to fix

perhaps I should have mentioned I have repaired fuel senders at the component level before

the "variable resistor" in those cases was a wound cooper wire coil on a flat board, with a wiper driven by the float (older vehicles)

current goes + bat>instrument>sender>earth

faults have included broken or dirty copper coil, failed float, or mechanical issue with float arm/contact blade

prior to pulling the assembly, I wish to verify the current flow path in the XJ, so I can make sure earth path is not broken (failed sender)

so if I unplug near the tank, and multimeter test between DB and sender, I should NOT see infinite resistance (sender side fault)

if I test for voltage between instrument plug side and earth, I should have a voltage (if NOT faulty instrument or wiring)

the most common fault I found is the copper coil is open where it is soldered..resolder, and you are back in business

you can imagine how grateful a Lamborgini owner was when I showed him how to make this repair