Hello,
I've been reading few thread about this issue. I couldn't find something similar to what happened to me.
Mine is a XJS V12 HE 1985.
First the Tachometer started to work erratically and then died. This is happened in parallel also with my cruise control...
I find this strange so I'm asking my self if they are combined or if they just work together against me!

 

I take it that everything else in the instrument cluster is working?
The tacho is driven from the Lucas amp on top of the B bank inlet manifold. The signal wire is a very thin white one with a blue spiral and it runs to a white bullet connector around about the coil somewhere. Check this wire and connector are intact first.
I am not sure how to test if the signal is being generated by the amp, but someone on here will know.
Whatever the test is, test at this connector first.
AFter that post again, as it will then be neessary to test if the wire to the instrument is OK, and after that the instrument cluster and tacho itself. There are loads about, so no bother if you need a new one.

The cruise control system, AFAIK is not linked to the Tacho at all. As long as the speedo is working then the signal for the CC is being sent OK. Do you have a CC diagram? But first off, check that the vac actuation line to the CC bellows is intact and that the bellows themselves are not leaking.

 

Regarding the tach, this might help. If you pull the bottom cover off

the amp you can check the resistors. This sketch is from the AJ6 website.
Can't help you with the CC, mine doesn't work either, future project.