Apologies for the cross-posting but I saw this on the XJR forum and replied to it there.
I had this problem on two year 2000 X308 XJRs, and in both cases it was the Brake Pedal Position (BPP) Switch. The BPP switch contains two microswitches, one for the brake lights and the other for the cruise control. In a thread on another forum I saw someone say their nylon quadrant had worn, and they’d glued a piece of credit card onto it to compensate. In one of my cases that was exactly it. I only had to depress the brake pedal a tiny amount, and I could hear the microswitches click. I glued a piece of credit card onto the nylon quadrant and that sorted the problem.
In the other case the C/C microswitch was dicky. I was able to get contact cleaner into the C/C microswitch and get it working again. As a precaution I glued a piece of credit card onto the nylon quadrant and was glad I did when I realised just how little the pedal needed to be moved to de-activate the C/C.
If the microswitch is totally U/S, it ought to be possible to replace just the microswitch with careful soldering, at a fraction of the price of a new BPP switch.
As an aside, although the BPP Switch is held on by just one bolt and a self-locking nut, it’s a bear of a job because you’re upside-down with your head in the foot well. Because the bolt is long, it’s a real pain running the nut off. I had no ratchet small enough to get in there. I was dead lucky finding a rubber bush which was a lovely tight fit on my ¼" drive socket, giving my fingers much more purchase, and the resulting tool made it a breeze to spin the nut off the bolt (and later back on again). I have photos of the disassembled switch if they’d be of use to anyone.
I might add that I don’t know why the Failsafe Engine Mode is caused by problems with the C/C switch, but they’re definitely linked. The first time I ever saw it, I’d tried to use the C/C and it wouldn’t work. Only after I’d tried engaging the C/C several times did the Failsafe Engine Mode appear. Whenever I’ve had the Failsafe Engine Mode, the C/C has been disabled, and the light on the centre console has gone out.