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#1
Instead of struggling with Cortana and Windows Search my preference is to use 2 third party software. I set one to only search my C drive and the other to only search my second drive. Both Everything and UltraSearch can search both drives if wanted, with UltraSearch you can very quickly include and exclude drives from the search Both are small, fast, reliable, very efficient and free
Everything Search
UltraSearch
Good luck :)
Again, you have to change the Security permissions for that other drive, by going in to explorer where it shows the drive for C: and most likely the old one as D: or whatever drive letter, then right click on the old drive, choose properties and then choose Security to change the permissions on the whole drive to your user ID>
I'm on the latest windows insider build and the feature seems to have made a comeback. It now displays all the files regardless of it's location in my computer. I did request for it in the feedback option in Cortana, that may have helped.
What version of Windows that you are using has zero to do with how your searches go. There are more powerful third party search programs out there that do not tell Microsoft what you are searching for. I suggest that you go to majorgeeks.com and look for a third party search program tat works a lot better than the search feature that Microsoft uses.
Cortona will tell Microsoft for their metrics how someone is using that program to search for stuff and how the OS is returning what may or may not have been asked for Windows search to look for.
I've tried a lot of those 3rd party ones and eventually stuck with Everything Search, but none of them is quite as effective as Cortana to search music files, which is what I do most of the time I hit up a search.
My main gripe with Cortana was that it forced me to click through filters to get results for files stored in other partitions and external drives, which was annoying cuz I run windows on a small SSD and store media on HDD. Now that it has been rectified, I have no problem using it as my only search tool notwithstanding the privacy concerns you've mentioned.
I'm assuming you've indexed all the drives you want to be included in Search Options. Even then, I've noticed that Cortana won't display results for .exe files that are not in the Programs List as well as many other file types. Just use Everything if you want a reliable search for everything.