Well, there is another option to search you can use which doesn't rely on Cortana search.
Click on This PC on your desktop.
Then in the file explorer window, the address bar will be This PC, opposite this is a search bar. You can use this search box and it will search your entire computer, including external drives, thumb drives, etc...
Alternatively, you can click on your external drive and then use the same search box to search just that drive.
This is how I always search on my computer.
If your drive still cannot be searched using this method, then there must be a problem with the drive. You could try and use the drive in another computer and see if it works then.
Let me know how you get on.