You should submit a bug report to Microsoft, and shame them over not using a variable to store the drive mount point, because that’s stupid.

I changed the partition letter back and Search started again. I then set the index location back to its default location; but I still can’t change the other partition letter without the search service stopping.

I found entries in the registry key: HKLMSoftwareMicrosoftWindows SearchGathering Manager – they still point to the moved location.

I tried to change those entries ‘DefaultApplicationsPath’ and ‘TempPath’ in the registry key, but don’t have permission, even after turning on the hidden administrator account and trying to elevate privileges for that key.

I can’t figure out how/why the registry entries changed, but won’t change back to the current default location.

I had turned the Search (and Indexing) feature off and on a couple times, as I have my OS on an SSD and read old recommendations to turn it off, but realized it is best left on.
I even tried to remove the Search feature and reinstall it, to no avail.
I could live with the non OS partition letter as is, but it is not an ideal solution.