The YouTube team is testing the Incognito mode on the YouTube app for Android devices. The new change, which appears to be rolling out for select users through a server-side update, is designed to disable the watch and search history from the active session. It has been spotted that a dedicated Turn on Incognito option will be available once you tap your avatar from the top-right corner of the YouTube app. This option will sit in place of the Sign out option as the latter will be mingled with the Switch account option.
The screenshots posted by Android Police folks shows that the Incognito mode on the YouTube app is similar to what we already have on most browsers. It notably transforms your existing avatar with an Incognito icon to notify you that you’ve not signed out but watching YouTube content under the Incognito mode.
It is unclear when the YouTube app will receive the Incognito mode for all Android users. Of course, YouTube already offers an option to pause watch and search history that you can access by going to Settings > History & privacy.