Yours is a bit newer than mine so it might be a different fuse under the bonnet, sure someone will tell you which fuse exactly.
If it is the pump, before paying Jaguar prices (£100+ roughly) check the part number, early S Types (inc mine 1999) used a Mondeo/Escort/Transit-Connect/Volvo S80 washer pump that can be picked up in generic form on fleabay for under a tenner.
If my guess is right and it is a Ford item, chancs are the part number will be along the lines of 86AB17K624DA or similar, here's a link to the early screen wash pumps :
https://www.ebay.co.uk/itm/252268529673
Hopefully just the fuse though! 😉 😄