I just figured out something - for those, who'd like to know more, I'll explain in detail below - for the others: Here's a spoiler:
Suddenly key would not start the X-Type anymore (it was my key number 4), and I found very quickly the reason: The transponder-pill inside of the key-fob had somehow "died" - I replaced it, and voilą...:

The picture above shows the transponder pill next to the key, which normally lives within the front part of the key-fob...

My advise number 1 is: Make copies of your OE keys! You should have received with your X-Type two ORIGINAL keys. If you should ever loose one of those two, you'll be buggered! This is why the first thing I always do about a new Jag is create a 3rd and 4th copy. Copying the REMOTE of an X-Type is quite simple, regardless how many keys you have to start with, but the key fob also contains (in the front part of the key-fob) a TRANSPONDER-pill or transponder-chip, and without that transponder, the car will not even attempt to start up. And to copy THIS TRANSPONDER, you'll need both ORIGINAL keys...

Normally, if you place the key into the ignition and turn it into position 3, you'll find that the red light in your centre console lights up red for an estimated 5 seconds, after which the red light will turn itself off again (at least on the 2001 X-Type, only which I had the issue at hand - I currently do not remember, if that thing about the red light is the same on newer X-Types).

But what I just experienced using my 4th key for the X-Type (which worked perfectly before): That red light did not turn itself off, but after those approx. 5 seconds it went into a continuous blinking mode - PLUS: turning the key from position 3 into START was to no avail, as the X-Type would not even attempt to start...

Now: My special situation was that I did not start THAT X-Type for about 1 year, I think, but I had the battery removed (before putting it back in for the occasion), but I was sure that the battery was doing just fine, as I has it sitting in the garage and I permanently recharged it with one of my CTEK chargers (15A).

Thus, if it's not the battery...: Why would the X-Type play possum? (meaning: why would it feign death)?
The only thing, which came to mind was the the transponder was "playing possum"...
Thus, I got my keys number 1 and number 2 (I have them all numbered) from the house: They were both starting the car/cat (and btw.: Perfect start at first attempt after about year, and it purrrred perfectly).

Thus, things were very clear now: The transponder-pill of key number 4 (which I self-programmed years ago - and I'll explain below, how), was non-operational.
The first logical conclusion would be that that pill somehow lost it's memory so to say - HOW such a transponder-pill works is an utter mystery to me...
Logically, I attempted to reprogram that transponder-pill AGAIN after all those years, but to no avail. It did not want to be programmed anymore.
Thus, I concluded that that transponder-pill had met it's maker (=is dead a a Dodo, it's now an "Ex-Pill/Parrot" (Monty Python)).
Luckily I do have a box with brand-new never before used Jaguar flip keys. I removed the transponder pill from one of those and put it into my key number 4, did the transponder-programming-ritual again, and key number 4 was good to go (no more blinking of the red light in the centre console, and that key could now also start the X-Type). The transponder pill in the picture above this THAT one, which is dead as a Dodo, but it does not look different than any other of those pills...
I do not have the foggiest, though, as to why this pill is dead, as I also have no idea, how it works in the first place...

And here as promised the programming ritual to DIY program a 3rd and 4th key for your X-Type, which works only, if you still have your ORIGINAL 2 keys, which is exactly why you should create a 3rd and 4th key, if you have not yet done so, and then only use the 3rd and 4th key to drive the X-Type and keep the 1st and 2nd in a save place at home...:

You simply insert the 1st ORIGINAL key into the ignition and turn it to position 3. Watch the red light in your centre console - The light should light up red (no blinking) and then simply turn itself off again after an estimated 5 seconds. This tells you that everything is alright with the key and it's transponder. Next you remove that key and insert the second ORIGINAL key, again into position 3, wail till the red light goes off (and does not blink) and then you remove that second key and insert the 3rd or 4th key (only one, then start from the beginning, if you have more keys), turn into position 3... - and : Finished. Now that additional key should start the X-Type just like the 2 ORIGINAL keys...

Note: I read on the net, that you should wait 30 seconds between keys - that is nonsense...

 

So where did you get a replacement for that transponder capsule? Just took one out of another key and then re-code it using the two original keys?

 

Yes, some time ago I bought about 25 of those flip-keys somewhere on the internet from China.
I got them for a very good price - and I just took a pill out of one of those.
Other than that I made sure that all my Jags have 4 keys. - Even the '98 X308 has 4 flip-keys - I had to file a corner off those flip keys to make the longer 8-code-Tibbe-key fit and I fitted the security module of a 2003 X308, to make the flip keys work to start with.

And yes: I recoded the new one using the 2 OE keys.

 

But what do I do if I only ever had one key?

I got a 2nd blank key from eBay for about $5 and found a person here on the forum who had a Tibbe Key cutter (Sone...are you still here?) who cut the key for me so I have what I call 1 and a half keys. If key #1 gets locked in the car, no problem. Key #2 opens doors physically and the key fob part works to remotely lock and unlock doors. The key part physically actuates the ignition switch but the little pill transponder doesn't work.

One day on a lark I bought a dozen random pill transponders on aliexpress for literally pennies each. Delivered to the US in several packages from several places but all from Khazakstan. Weird. None of them worked but I was literally invested under $1 US.

So I still have 1 key that works and 1 key that does everything but start the car. I would love to know how to have 2 actual working keys.

 

For X-Type: If you have just 1 key, you need to go to a specialized locksmith, who is able to clone those pills. He will probably not be able to clone the function of your OE pill onto the pill in your new flip key, but he should be able to clone it into a chip, which he has in his shop - it's just a small chip, which you then place into the flip key instead of the pill. And DIY remote programming should not be a problem on the X-Type - you just need to press the buttons of all your keys in one session.

 

Cloning is one option
A high end key programmer or scanner tool can also add the keys to the internal approved list.

I did with the SSD 1.63 tool ( If I remember right) bit scary as it effectively locks/removed previous entries and you add all you keys back in
The same tool would also show you current number of keys programmed and previous reprograms.

TIA

 

In my original post on top I described the DIY programming of the transponder.

ABOUT THE PROGRAMMING OF THE REMOTE:
It's also an easy DIY exercise to DIY copy the remotes. For that it is not even required to have the 2 OE keys. Note, that it may be necessary to also reprogram the remotes of the OE keys as well, when you program the new keys - all in one session. Just try to do the 1 or 2 new one(s) first only, and then check, if the old ones still do work - if not, do all 3 or 4 in one session. That "session" is described in the pdf link attached.

AND ABOUT THE TIBBE KEY BLADE:
Reg. the blank tibbe key blades: Either find a local locksmith, who is NOT overly greedy (where I live, there is only a greedy one), or - do as I do:
I found a cheap, good and reliable locksmith in Melbourne, over 2000km away:
I just remove the blank blades from the flip keys and I don't even need to send him the OE blade - just the blanks, and a very good picture taken of the side of the OE tibbe key blade, because, you can actually "read" the code yourself. You'll find instructions, how to read the 4 digit code (for X-Type / the X308s have 8 digit tibbe keys) on the net.

BUYING NEW KEYS:
I am fairly sure I found those complete tibbe keys back then on Aliexpr. - be careful there that they do not trick you. You might believe you are ordering a complete key, but then you get only an empty shell. just click all the options, that one seller has - if you do not click the options, they might display the complete key, but send you something totally different... - I just check on Aliexpr. - I entered the key words "Jaguar flip key" and without extensive search I found one for under AU$25. You may find a better price, if you search long enough. But as I mentioned before: Be careful about what exactly you are ordering there. I found a listing, which looks like the complete key, but it said "no chip", which is the same as "empty shell". Also, some let you select between 315MHz (for the US) and 433MHz (pretty much the rest of the world). If you select it when buying, they press a few buttons for you on that remote before posting. Otherwise you can press those buttons yourself - all those keys should be suitable for both frequencies, you just have to select YOUR frequency.