When you say "media-indexer", are you referring to Spotlight, or to the old app called Media Indexer from Alorsoft?
In either case, depending on the size of your high drive, and how much data you have on it, yes, it could take a good while for it to index your entire disk.
Also bear in mind that if you have any external media attached to your machine, Spotlight will index those too, unless you tell it not to.
You can do this by opening the "System Preferences" app under the Apple menu in the top left corner of your screen.
Once the "System Preferences" app opens, click or tap on the "Spotlight" icon.
When the "Spotlight" prefs pane window opens, click or tap on the "Privacy" tab.
As you will see, you can use the "+" button to add locations which you do not want Spotlight to index.
In fact, if you have external drive icons on your desktop, you can just drag then into that window, and they will be added to the list.
When you are done, just close the Spotlight window.
If this info has been helpful, or resolves your issue, please let me know. Thanks!