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I had a charging system fault pop up a couple days ago and traced it down to the charging system monitoring module that is integrated with the ground (earth) connection at the battery. For some reason the rubber at the base of the connector had a tear in it and the leads inside had suffered from fatigue failure. Perhaps caused by the numerous test fitments while trying to deploy a Lithium battery. Be careful with that part. Retails for more than $100 (Online for about $80 delivered).
That's some good troubleshooting on the OP's part. Good reminder about many sensors being generic/non-Jaguar. Like virtually all automakers, Jaguar doesn't make its own sensors. They pick one from a catalog, which means that it's used on other cars, often ones far less expensive. For that reason, it does indeed pay to look at the sensor to find the manufacturer's name and part number, then do an Interweb search to see what turns up.
The manufacture’s part number brought up some used eBay parts at about $45 and some Chinese new parts at ~$65. The extra $15 worth not waiting 5 weeks. I don’t like to risk used electronic parts.
i’m not certain the OEM unit is actually a Bosch. You can search the Interwebs to see what they cost. eBay has them for 69+ freight. Here are the LR and Jag part numbers:
Based on your thread it could be a number of things. Here’s my suggestion:
1. Borrow a known good battery. Doesn’t have to fit properly. The cables just need to reach the terminals. Make certain you fully brush out and clean the terminal clamps.
2. if that doesn’t resolve the problem, it’s probably the voltage regulator. Unfortunately that requires a full alternator replacement as the regulator is integral to that unit.
3. if it’s anything else it will require more complex diagnostic equipment than I know how to use to track down.