HI
On these make sure you use ZF original parts and ZF Lifeguard 6 oil, you usually get a kit, which includes 7 litres of lifeguard 6, filter/pan, new pins for the pan (usually the heads are bigger as oe ones were too small, new mecha sleeve (seal over the connector, prone to leaking), there a specific procedure on these for changing the oil, car has to be level and the final oil level check needs to be exactly when the gearbox is at 45 deg C, as it effects the oil level, also the gearbox holds about 10.5 litres, but at least 4.5 litre of that stays in the torque convertor, hence why its bad always mixing different types of oil. also a lot of after market filter/pans tend to leak. They should have the gearbox oil changed every 60k or 10 years, thats what ZF recommend.
Symptoms of common problems of the S-type ZF 6HP26 are harsh shifting inbetween gear changes and surging when cold at around 30 to 40 mph, surging can also be fixed by a software update to the gearbox, if its never been done, but last update on these was 2009, so most have been done.
If running right they should be silky smooth in normal mode
if you want to do some reading, theres lots of info on S-types and S-type R here http://www.jagrepair.com/
This video shows you exactly how to change the gearbox oil on these. https://youtu.be/MAMseFY8GpY?si=G6j6zNd3FwExftY6
The S-type R is really a great car, love mine, mine has been very reliable and never given me any trouble, but it does get well looked after
if your after any other info just let me know, I gathered quite a bit of info over the years on these.
cheers
Joe