This is a video of my wife taking a solo drive in the XJ-S. She doesn't drive it very often but hasn't really complained when she does. Maybe she finally likes one of the cars I picked?
As you watch the video, you'll quickly notice that the car doesn't appear to start very well. Why is that? An XJ-S owner in Pennsylvania told me it's because the battery is located in the trunk. From his perspective, this made the electricity travel too far, thus giving the starter a hard time. Yes, it's a strange location (until you see how much room a V12 engine takes), but I'm not yet convinced that's the problem.
The other idea came from the guy who sold me the car. He opened the center arm rest compartment and pointed to an ignition module. He said something like, "You don't really need it, but if it's hard to start you can re-install it." Hmm, do you think that might be the problem? That may or may not be the entire solution as the early V12s had trouble starting after being driven and then sitting for an hour or so. For instance, when I start the car in the morning, it starts on the first turn of the starter -- almost instantaneously. However, if I've just brought it home from work, and let it sit for a while, it does exactly what happened to Sharon.
I'm sure there's an explanation out there somewhere (maybe in Kirby Palm's book), but I haven't taken the time to find it yet. In any event, it's not a huge problem as it usually starts after a few lengthy attempts. Not to worry.