Roger
Even with a new battery, which is good news that the seller replaced it, you should still consider buying a CTEK to keep the battery in good condition. Jaguars are notorious for battery drain.
Best Wishes, John
I think Jaguar in general is "very unforgiving of low voltage." My S-Type needs regular use of my CTEK MS 7 to keep it electrically fit. One of the best investments I have made in looking after my S-Type, especially for the relatively low cost. I put mine on charge at anytime when I know it is not going to be used for a couple of days. If it is used daily it still gets put on at least twice a month.
Best Wishes and Regards, John