The old memory just ain't what it used to be.......
I finally got thru the archives and sure enough, confirmed that Jaguar did not have a security system available for the 1988 models. The 1989 models did have one available, but only as a dealer installed accessory. A factory installed system came in 1992, though it could still be installed later if not done at assembly. In 1993, early cars had the dealer fit system installed at assembly, and later cars had a factory integrated system as standard.
That doesn't help you much, Jenny. Which means anything in your car is an aftermarket system of some sort.
Cheers,