Eureka! I managed to get into the programming mode in my 1996 XJS. The computer beeps are very hard to hear if you are in the car with the windows up, but nevertheless, I stripped and shoved a bare wire tie in the yellow with white wire and another in the black wire harness hole. I turned the car on (but not the engine) connected the two wire ties, then shut the car off and quickly started tapping the wire ties together. It takes more than 4 or 5 taps, but not more than 10.

Here's the problem. I think my second fob is DOA. I definitely had to press my current fob 5 times to get out of programming mode, but it would not recognize the second remote.

They are both 318Mhz. I did change the battery.

Is there any way to check if it is indeed working? Any help would be greatly appreciated!

 

Actually, upon second inspection, it is indeed a 433 MHz.

Rats. Looks like it was $70 misspent.

Let me know if anyone needs a brand new replacement for $70.

 

Well, it's done. I've successfully added a second FOB to my
1996 XJS.

I had issues finding actual Jaguar remotes cheap enough to experiment with, so I bought one from a third party vendor on eBay for $22 shipped. I
figured it was worth a final $22 experiment.

Took out the center console, shorted my way right into
learning mode and the remote took without any special
coaxing or trickery!

I wanted to follow up once and for all and confirm that
programming a new fob for a 1996 XJS is, in fact, simple to
do from home without the need for a Jaguar dealer or their
machines/computers.