Hello, I have the 1997 XK8. I, too, am facing this issue. I realize your post is 2yrs. old, but thought I'd share with you my experience. Reaching down and following the cable with my hand, I managed to locate it to a harness behind the throttle body, near the firewall. It has seven wires, and my harness is pictured in the attachment. I have also attached a photo of the neighboring three harnesses which are a bit higher up and easier to see, but the one that goes to the rotary switch is the black one.
Did you ever have luck removing and replacing your switch? I would be interested to know what symptoms you had, and if this resolved them. Right now I have an Engine Fault that only happens after I drive the car a short way and shut it off, after which it will crank but not start, with a P0790 code.
