Unfortunately, this could be a more difficult problem than a simple wiring issue. If ground/continuity is not the problem then it could well be an issue with the SLM (aka SLCM).
This is the security module for the X308, but it also powers the tail lamps via integrated circuit amplifiers on the SLM board. Unfortunately, these are known to go bad, causing intermittent rear light failures until the chip fails completely.
There are three chips, one driving the left side lamp, one for the 3rd brake light in the middle, and one for the right lamp assembly if I recall correctly. If one of these sets of lamps is the one consistently failing, then it could well be a failure of one of the amplifier chips (less likely that 2 or all three are going bad at once.)
A replacement module could be expensive, and needs programming by the dealer if I recall. You might be able to get one from the junkyard. To do so, look for a label in the trunk on the left side floor (near the CD changer if I recall correctly.) This is called the “VCATS” label. There is the vehicle VIN, followed by a list of modules and serial numbers next to them. One of the modules will appear as “SLM.” If the donor car has the same serial number for “SLM.” as yours, then you should be able to use that module.
There’s no guarantee the junk module doesn’t have a burned out amplifier chip as well. But, if you are good with a soldering iron, you can replace the IC amplifier since the chip is a standard one (though one that seemed to become hard to find.)
I was going to attempt this repair once I found a suitable junk module, but my XJR met an untimely demise before this could happen. So I never did it.
Hopefully I recall all the details accurately, but if you want to try this, here’s the link where I got the info from. You can verify/correct any information from there. https://www.jaguarforums.com/forum/xj-xj8-xjr-x308-27/passenger-side-rear-brake-light-not-working-already-replaced-bulb-10830/page5/
Dave