Hello  @Prnorth 

- Please try to remove Schedule / Away Mode/ Timer/ Smart Action/ Scene settings on smart device  in case those settings affects the smart device:  
How to setup schedule, away mode and timer of TP-Link Smart Plug/Switch in Kasa APP?

With schedule settings removed, does any  plug turn on by itself? 

- If it works with any third party smart app , like Alexa /Google /Home automation etc., please unbind or remove settings temporarily while test 

- If the unusaual  behavior is  with certain plug, factory reset it and see if the same happen again. 

Factory reset kasa device and reinstall it on Kasa app and see if issue is gone

How to reset TP-Link Kasa smart switch and plug?

If still the same issue,1) please describe phenomenon  as detailed as possible,   e.g. at 8:00 UTC+1, xx light turn off by itself and stay off, power led on plug went off, need manually press power button to turn it on, or turn it through APP 2) share the mac address of the smart device to us via private message.