LairdScooby

If it appears mostly after a start after a period of inactivity then i would suggest the battery voltage is getting a bit low. Keep an eye on it and see if that's when it mostly comes.

What Joe said ^^^^^ I suspect it's had a change before and the wrong fluid was used, alternatively it could simply be the original fluid is old and dirty. It's surprising how many faults are fluid related. Also worth checking the wheel balance on the back end and also springs and dampers/shock absorbers and suspension bushes at the back end.

Manual or auto Kim? Engine, petrol or diesel? Any fault messages on the dash?

First port of call would be a JLR dealer for preference. Next Timpsons - i believe they can now decode your existing key and fob and supply new, programmed replacements. There may be other suppliers online that can reproduce the key and fob, worth an internet search.

That doesn't sound like an EGR related problem to me, more like a DPF or fuel supply problem. Try https://superchargedperformance.co.uk/ in Bury St Edmunds, to my knowledge they've sorted a 2.2 XFD and a Range Rover 3.0 V6D with good results

Overtake

Check your front tyre pressures and then if you don't find anything, check the front dampers (shock absorers) and front suspension bushes. Also have the wheel alignment checked - all of these things can cause the steering to go exceptionally light at speed.

First, get your battery charged up - you won't be able to trouble shoot with a flat battery. Then when you turn the ignition on, check for a charge warning light - if the bulb has blown it won't charge, also see if it has an internal or external voltage reg as that will alter the method slightly for diagnostics.

Welcome aboard Tommy!

Try looking for a Nissens brand on ebay for your car Paul - they manufacture most of the aftermarket (and many OEM) radiators. They may not have an uprated version but that's not necessarily a bad thing! If you have an excessively large volume of cold coolant in the rad when the 'stat opens, this can cause other, very expensive, problems.

Force

I'd read the DTCs first before you fire the parts cannon at it. It sounds like the whole bank is effected so i'd look more at a fuel delivery/pressure problem on that bank and as a general bit of maintenance, run some injector cleaner through it.

Susceptance

I'd have a look online in your home area (it says non-UK so no idea where in the world you are) and find a Dexron VI compatible fluid and use that, especially if you plan on periodic part-changes or full changes to maintain it. A quick search revealed that Pentosil #1 is a "life-time fluid" so is likely to be more expensive and won't necessarily last the life of your box. I'd prefer to do a part-change once a year or so to maintain the fluid than use a "lifetime fluid" that maybe breaks down and kills my gearbox. Each to their own though.......

I believe the later S Types use a ZF gearbox so you should be fine with a Dexron 6 fluid or equivalent. Is there a reason cited for the use of Pentosil #1?

Depending where exactly the material has come loose, you may be able to make an in-situ repair using adhesive carpet spray - hold the headlining away from the backing board (biscuit) and spray some glue onto the biscuit. Let the glue "flash off" then carefully and progressively fit the liner back onto it. I've used this trick on many cars over the years and it usually works well. However, if yours is truly horrible, you may have to bite the bullet and take the complete headlining down.

Nervous

Panic

Claustrophobia

Little tip with the inertia switch - tap the body of it with the handle of a screwdriver until you hear it deploy with a definite "bah-doy-nnng" then reset it. They have a habit of furring the contacts, especially if sat for a while and this can often cause the fuel pump to not run. Also try the spare key in case the transponder in your main key has died.

The fuel pump isn't always noticeable when you switch the ignition on so i'd suggest you get someone who has the necessary diagnostic equipment to troubleshoot. You could spend a lot of time (and money!) firing the parts cannon at it without getting any results. It may be something much more simple like the CPS (crankshaft position sensor) causing your non-start.

What diagnostics have you done?

Timeline

Welcome aboard and if you don't mind sacrificing a spanner to make it an "S" shape, it apparently makes changing the oil p sender much easier. Not done it myself but saw such a spanner ~25 years ago in my local Jag specialists when i was buying a car from them (XJ40 3.6 Sovereign) - luckily mine didn't fail during my ownership.

Digital (Digital Disarray was the name of a website i used to visit occasionally many moons ago)