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I have often wondered this as I have replaced probably at least 50 or more just between the X308 and X100 cars. I believe it's from the pumps themselves slowly shorting (failing) internally and creating more amperage and overheating the wire?? I might be wrong, but I'm sure someone smarter than me will chime in.
You obviously have a short causing a surge you need to trace. I'd be more than suspicious one of your body grounds isn't connected, thus shorting your fuel pump wiring. Another possibility would be a pinched and/or bared wire leading to tank or your fuel pump itself burned out and shorted.
Highorse, the wiring harness between the fuel pump and the underside of the fuel tank lid is a sealed box... Do you know if there's a resistor inside that sealed box??
I had to dig around a bit, but this is for a 2001, which I believe is the same as an '02. I don't see a resistor listed...it appears to be a basic activation.
The black sealed bit is a radio suppression circuit.
It is best described as a LC circuit which someone else
can explain. The patent drawing is available on the internet.
Denso patented a radio suppressor built into the pump itself,
so Walbro, the OEM for the Jaguar pumps could not use the same
arrangement. To be competitive they introduced the outboard
radio suppression circuit and patented that.
If the LC circuit is on the ground side and the ground stud is
always the one that goes brown, then I would suspect that
the LC circuit is causing it due to resonance. Or, something
as simple as the added weight of the dongle loosening the
spade connection creating higher resistance followed by
heating/charring.
I just tossed mine and had it replaced with fuel grade Teflon
insulated wiring.
A clogging fuel filter could also cause the power required to pump fuel to increase and lead to higher than normal 'amp draw' on wires not rated for it.
Jaguar recommends fuel filter replacement every 30,000 Miles.
A worn pump AND a clogged fuel filter will likely draw some serious AMPS!!!!!
Sometimes the simple answer is the most likely answer
Funny if its always the one side of the circuit though.
Currently leaning towards the black box being left to
dangle. Much simpler than analysing the effect of the
LC circuit on a power circuit