Z Car Depot shows a bushing (parts 63 and 64). The photograph of these parts appear to show them as rubber. Looking at my 260Z I think I'm missing them. If so, that may explain all the noise I'm getting from back there.

Uh oh. It looks like the clamping bracket has fallen off. You can see the threaded hole for the bolts. You'll need the bracket and the bolts. @Terrapin Z might have what you need. Parts 70, 46, and 47. Bracket, washer, bolt.

Here's a few pictures from BaT. What should be there. Better check the front also, looks like it's loose or gone also, allowing the displacement. The diff mount crossmember does the job up there.

I took the bracket off to inspect the bushing. So that's not an issue. The bushing is rubbing metal on metal on the bracket. Is that correct? Z car depot shows a rubber part.

The factory bushing is rubber formed around a metal tube. Aftermarket PU replacements are a separate tube with two PU bushings.

The factory part has metal teeth on the ends of the metal tube. Looks like the rubber might have left your bushing. The tube can be difficult to remove from the control arm. Big pliers or vise-grips might be necessary.

https://www.tascaparts.com/oem-parts/nissan-bushing-rear-55555e4100

Here's an example of the aftermarket parts. I'd just use the factory rubber. Better ride.

https://www.rockauto.com/en/moreinfo.php?pk=6397113&cc=1209226&pt=7532&jsn=448