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My 1993 XJ-6 has a rattle coming from the passenger side control arm. The rear most connection on the differential can be moved up and down about 5mm. According to the schematics the part I need to replace is a MTC 7886 / CAC-4713 Subframe Bushing, located in a wishbone assembly on the back of the rear dif. Question I have is does this procedure require removing the entire rear suspension from the vehicle? Or can it be done on a "local" level? Any information appreciated.
CAC4713 is the correct part number for the lower pendulum bushes, Part 20 in the diagram below. The pendulum is the six-sided brace on the front of the differential, Part 18. But from your description you need to replace the bushes in the wishbone tie, Part 7. It's likely that they are the same part as the lower bushes in the pendulum, but that is not confirmed at jaguarclassicparts.com.
It is quite possible that you could remove the differential struts (Parts14) and the wishbone tie without dropping the entire independent rear suspension, though you will have to remove the long fulcrum bolts (Parts 2) which pass all the way from the wishbone tie through the pendulum and help hold everything together. It would be prudent to support the rear subframe to ensure things don't shift out of alignment when you pull those bolts (off the top of my head, I don't think they would shift far, but they might shift far enough to make reassembly difficult).
Worst case, it's not that difficult to drop the entire IRS. See photos of that process in my photo albums (link in my signature).