David,
(a) There should be two horns - probably a legal requirement to ensure there's a backup.
(b) Look behind the front bumper. Check the wires. Get someone to press the horn button and listen to determine which horn is not working (you probably want earplugs or defenders or something!). If nothing is obvious, you can remove the horn and try wiring it directly across a battery - horns are simple: apply power, they should hoot. If not, AFAIR there's a set screw and locknut, and you can adjust the set screw to get the loudest noise (or none if it's wrong), but probably the coil will have burnt out. In the latter case, you can buy cheap replacement horns at Halfords or a motor factors or off the Internet. Halfords show some Bosch horns for a 1995 XJS:
https://www.halfords.com/motoring/car-p ... 68678.html
though IMHO a bit expensive and online-only ordering. The usual suppliers (Jaguar classic parts, SNG Barrett, David Manners, etc.) can almost certainly supply horns at a range of prices.
(c) Somehow you've managed to post in the XJS forums but not in one of the normal sections such as Electrics, which means the "Board Index" web page shows a red symbol against the XJS forum, but no green marker against any of the subforums, so people will miss your post. I'm not sure how to rectify this - whatever, I've given you an answer! But next time, whatever you did to create your post here, do it differently so it ends up in say the Electrics forum. (Sorry not to be clearer, but I've no idea how your post ended up in the main forum - I assumed that was impossible!)