I'm not getting on what basis Google Play will update apps when auto-update is enabled.
Is it time-specific, or something else?
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Adding to @Josh's experience mentioned in the comments above, the auto-update is not time-specific - I too have only seen the auto update proceed when on WiFi (my chosen setting) and plugged in charging. On my Sony Xperia running Android 7.0, it appears to be the default behaviour.
I can't find any more reliable sources for this behaviour, but there is lots of personal experience: http://forums.androidcentral.com/google-pixel-pixel-xl/747707-auto-update-apps-while-charging.html
Annoyingly, it is not mentioned on Google support, and I can't figure out how to give feedback to them about it: https://support.google.com/googleplay/answer/113412?hl=en-AU
I can only post 2 links in this answer, but the 'WiFi and charging' requirement has been requested as a configurable feature (google 'how-to-allow-auto-update-of-apps-in-play-store-only-when-plugged-in') and there may be a workaround to achieve similar behaviour using the WiFi on Sleep setting (listed on benjaminoakes dot com).
My phone's Google Play app auto-updates around 1:30 a.m. daily (phone is never plugged in at that time), so there is definitely no connection of update with phone plugged in.
Phone must have WiFi on (selected in Google Play settings) for update.