Mozilla is working on bringing a new feature which will allow users to set a custom search engine for private browsing. The feature which was first added to Vivaldi will allow users to set the search engine separately for private browsing.
This is a particularly useful feature since it will allow users to select a more private search engine for private browsing. If you want to try it out right now then you will need to enable “browser.search.separatePrivateDefault.enabled”, “browser.search.separatePrivateDefault”, “browser.search.separatePrivateDefault.ui.enabled” in about:config. Once done you can head to Options>Search>Use this search engine in private windows and select from a variety of search engines.
As you might have guessed it by now, the feature is currently available to testers and is not publicly available. Mozilla, by default, uses Google so it will be interesting to see if the company decides to select another default search engine for private browsing.