Well , looks like battery time
 

Had to move the cars around today so took the opportunity to take the car for a ride. Ran at 13.5 V for a while but started to drop down to 13 , then 12.7 , then 12.6 and stayed there until I came to a stop. Voltage at idle at a stop went back to 13.5. So I came in and pulled out the previous owners service records and the battery was replaced on 4/24/14. Interesting though I have had no other mysterious gremlins show up. I usually take it to the dealer in April for it's annual oil change and NYS inspection so I'll most likely do the battery too. I just turned 24K so I got about 18K miles and 5 years on this battery. Also it's a OEM Jaguar flood battery so just putting back the same . Gotta get ready for top down weather. Enjoy the ride.

Yep, looks like time for a new one and then time for a CTEK.

More important you're thinking of being ready for great "top down" fun when it finally rolls around!

It's been on the Ctek since I got it. back in 2014

Good move.

I would have thought if the car was running it would just show the alternator voltage. If it wasn't then it sounds like it could be the BMS doing its self calibration routine:

Periodically the BMS module will instigate a self-calibration
routine. To self-calibrate, the BMS first charges
the battery to its full condition.

Once the battery is fully charged, the BMS will discharge
the battery to approximately 75% of its full state
of charge, but never lower than 12.2 V. The time taken to
complete this part of the routine is dependent on the
electrical load on the vehicle and the length of time the
vehicle is used.

When the second part of the routine has been successfully
completed, the BMS will return the battery to its
optimum level of charge. The optimum level of charge
will be between 12.6 V and 15 V, depending on battery
condition, temperature and electrical loading. This process
is run approximately twice a year.

NOTE:
If the vehicle is only driven for short periods the
self-calibration and charging process could take a number
of days to complete.

I was thinking the same thing when I read this in the manual but didn't know how long this process takes. I'll get a better feel next month when I drive it to the dealer. This is a 1 1/2 hour drive and will cover ranges from 30 mph to 70 mph. If it's the re-calibration then I should be back at the 13.8 V steady at speed. We'll just have to wait and see but at 5 years maybe it's just worth while having the dealer change it. They usually give me a overall systems check at the time of the oil change so if the battery is down due to age they'll let me know.