We bought our 2012 XJ almost 10 years ago (2015 ), and of course when we left the lot there were no faults; at least not until a few miles later. Then the TPMS fault notification came on.
Of course we took it back the next day, but they cleared it and said they couldn't find a problem. It wasn't a Jaguar dealership, just a used car place.
It was cleared when we left but came right back up miles down the road again.
So...
A few years later while at the dealership for an oil change we had them look into what the fault might be. They looked at it for an hour or two, said they couldn't figure it out, then said with a couple more hours they could remove the driver's seat to access the TPMS control module & check it out.
We declined since it was already a waste of 1 or 2 labor hours with no results.
And since then still have been driving (fine of course with no tire failures) without TPMS and just getting the TPMS fault warning with each start.

So anyway, I bought a full set of VDO TPMS sensors from Rock Auto a couple of months ago to replace whatever was in there - I figured maybe there was one of the 4 sensors that was different since that would be enough to trip the fault, or something of the sort.
Well today I sprung for the $77 bucks to have a Pep Boys change out the sensors (Costco refuses to mount any TPMS Sensors they don't provide, and they don't have any that are compatible with the Jag or my Range Rover, so...)
I was a bit surprised to find that none of the ones they removed were original Jaguar TPMS sensors since it was only 2 years old when we bought it (from a used car dealer), in fact all four were some cheap aftermarket brand - "Alligator". Not only that - they were marked "434 Mhz" (433 Mhz really?) which is not the correct frequency for US market TPMSs.
I did try to find what I could on these "Alligator" brand TPMS's. On Ebay I found some, also 433 Mhz, and according to sellers listing they are a fit for my 2012 Range Rover (and 2012 Jag since fitment would be the same)...
But they aren't. We need the 315 Mhz.

Odd, but finally that slightly annoying little TPMS fault on each start-up is TCO'd, for what it's worth.

 

That is super weird that the TMPS sensors were changed out at such a young age. I can only imagine that the previous owner swap the factory wheels for something else and moved the sensors to the new wheels, and maybe sold the aftermarket wheels with sensors whole and just put the cheapest sensors they could find back into the stock wheels.

 

I'd bet you're right. Somewhere between the first owner (it was a repo), the auction and the dealership the wheels were probably swapped back & forth.