Price sounds about right. The cars are very reliable but can get expensive when things go wrong and you are reliant on a garage to repair them, no different than any other high end marque.

I'd be reluctant to rush into buying any used car and want a thorough road test followed by an inspection at a Jag dealership. If this one doesn't pan out, another car will be along soon.

 

Oil leaks, coolant tank, if the steering wheel makes a squeak noise when turning, hard shifts from the tranny (lurching), water in the trunk under the spare tire, broken or cracked defrost panel by front windshield, tranny bolts that attach underneath were the cable connect to see if loose or missing, wheel balance (all 4 of mine were bent causing vibration),

 

Tires tread depth as new ones will run you about $1000usd.

 

Demand $13000, then let's talk mods.

 

It's difficult for us in the states because the prices are a good bit cheaper here. A car like yours has sold on EBay for in the $10K range or even less.

This one sold for $6500. It's a 2003 STR 129K miles
Jaguar : S-Type Jaguar : S-Type | eBay

This one was only $3600 but had a busted engine. Looked like a sweet deal to me!
Jaguar : S-Type Jaguar : S-Type | eBay

Here is a 2003 for $11900 77K miles from where I purchased my 2005 STR several years ago.
Used Luxury Cars | Mercedes Benz | Jaguar | Land Rover | Dallas, TX
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clubairth sums it up in a nut shell...$12,500-$13k max