Found a discussion on this on Apple's forums, confirmed their fix works.
https://discussions.apple.com/thread/8543734?page=2
In short - after upgrading to Safari 12, the spotlight search field disappears after typing 2-3 characters. Disabling the "Bookmarks and History" category in the Spotlight preference pane resolves the issue.
Question I have - does anyone know how I could uncheck that via script? I'd like to fix it for all clients, and it appears that the key is a bool value in the user's com.apple.Spotlight.plist file, but so far I haven't managed to find the correct defaults write key to change it.