What happens if you start the car, then unplug the CTS and then jump the two female plugs on the harness?

It's odd that the car wouldn't start with the harness contacts jumped, since it would be reading a warmed up engine....

 

An update...I got taken away by a higher priority vehicle this summer and so have neither fixed nor driven the XJS this year. Sad about that, but that's how things go sometimes. Update:

CTS - mine has a single wire so I wasn't sure how to test.
Spark - using an inductive timing light, I see that all six fire at idle but when I increase revs to about 1500, plugs 1 and 6 stop firing...which is why it won't rev higher and why unburned gas is making the cats glow (does that make sense?).

I replaced the ignition amplifier but that made no difference. Coil is in spec, and the ignition system works at idle. So now I'm wondering whether the problem isn't between the components, ie. a damaged wire. Mice have been under the hood. Also this idea seems to jibe with how the problem began--with the car parked for 10 weeks, having worked perfectly when parked. I don't see anything obvious so will have to dig.

 

I had a similar problem on the X300. It was a crankshaft position sensor.

 

Hi everyone, car is fixed...I thought that if the car runs, it's probable not the CPS, and if you see the tach needle moving when you crank, then it's probably not the CPS. Well, it was the CPS. Got a nice German-made DBC11501 from Welsh https://www.welshent.com/Engine/Jagu...k-Speed-Sensor and that's that.

Vee--I said a stupid thing up there, my CTS has two leads of course and that test didn't make any difference but thank you.

 

Just to add...the sensor itself probably still works, but the little sensing pin on the front face was corroded. Uncanny really--there's only the slightest surface rust anywhere else on the car but this was enough render the car unusable.