Don't have a remote FOB for your 1996 xj6/Vanden Plas ?
Does your car use the 433mhz remote frequency ?
If it does here is the best solution.
Just buy a cheap after market alarm system. This gives you a brand new remote and not a $100.00 used ugly Jaguar remote.
How?
In these cars if you ground the door unlock wire the doors unlock and disarms the alarm and unlocks the trunk etc.
If you ground the lock wire the doors lock and arms the system and locks the trunk etc.
Any inexpensive after market alarm system can be simply patched in to this system and will operate the factory security system. No programing. No fooling around with your car's security system. It's a done deal.
Check out the link I posted. Now I've found this system perfect. It's tiny, cheap,easy to install, and will roll up your windows with the remote when you press the lock button a second time and hold it. There's no need to install the siren or all the other features(unless you want to). I didn't. Your factory system has all that.
Soundstream Car Alarm 3 Channel Keyless Entry Security System 4 Button | eBay

Now if your car uses the 315mhz system there are the cheap Saab remotes available. You can buy one and just program it to your factory system.
Saab doesn't make a 433mhz remote. So I was stuck.
Also there are those Chinese cloning remotes which can be cloned to a working Jaguar 433mhz remote. That is if you have an original or can borrow one.
Personally I don't like the idea of someone out there with a remote that will operate my car.
So now that we know how simple the 1996 Jaguar xj6 system works go buy that after market alarm system and be happy like me.
Here's all the wiring : Do it yourself or let a pro do it. Either way it's simple.... problem solved.
1996 Jaguar XJS Stereo Wiring Information

 

1996 Jaguar XJS Alarm, Remote Starter, Keyless Entry Wiring Information

 

I see this is an older thread, but this is great info because my 1996 XJR uses the 433 frequency for the key fob. Any thoughts on how one would do the same thing with a 2 way alarm so it could page you if it went off? I was looking at the electrical diagram for the factory security system but was unsure where you would connect to trigger the paging alarm. I was thinking maybe the siren output but wasn't sure.