I have a privately published node that is updated correctly with the new version on npm, however I'm unable to update it via the palette manager 'update' button.
I've gone through the publish instructions but still not able to see the update button.
How would I go about getting node-red to look for new versions of a private npm node?
The palette manager uses the catalog published by flows.nodered.org to know when there are updates available.
If your custom node is not in the public catalogue, then Node-RED won't know about any updates you publish.
One option would be to create your own catalogue (a URL that serves a JSON object) which you can configure Node-RED to use via it's settings file in addition to the community catalog.
Can share more pointers if that's a path you're interested in.