Spotlight Search displays "Indexing..." forever macOS 10.12.6 

Spotlight Search, when I start to type, it changes from a single-line text field to the real-time search results.

In the left, between the bar and the "Top Hits" search results, it says "Indexing..." and displays a full horizontal bar.

This never advances (it looks full), and it never finishes.

The search results are not correct since this started happening.

I was suffering from the Safari 12 -> Spotlight Search display disappears while typing problem, and I've turned off the Safari indexing already.
When you say "never", how long? Indexing can take hours on a large mechanical hard drive. This is usually required after an OS update.

You can restart and rebuild the Spotlight index, which may help. Either use the Terminal command:

sudo mdutil -E /


(You'll then have to enter your admin password. If you've never done this before, you'll see a short warning about being careful.) 

Or go to System Preferences > Spotlight, and in the Privacy tab, drag the system volume to the list of exclusions. Then remove it.

Hanging Spotlight indexes may also be a sign of a failing hard drive, so it's also worth checking that your system volume is functioning correctly.