Random inverter turn on?

[JimFeet]

The inverter sometimes seems to come on for no apparent reason in my newly delivered 2021 Roadtrek SS-Agile. Unit has been parked in my drive while I outfit it from my original 2015 SS-Agile. Sunny weather has allowed solar to keep the Li-ion battery up to 13.4-13.5 volts but late in the day I have sometimes found the inverter is on and the battery has fallen to 13.2 volts. I'm confident it hasn't accidentally been manually turned on and am wondering if the low ambient temperature (under 34 F) is bringing on the battery heater and if that's what's turning the inverter on for some reason. The first time this happened the inverter draw pulled the battery down significantly before I discovered it a couple days later.

EDIT, I just found that shutting off the engine turns ON the inverter! What??? Why would it do that? I don't know but it does in my rig. Starting the engine doesn't turn on the inverter, just stopping the engine. This means every time I stop I need to remember to shut off the inverter. This makes no sense to me.

According to the Roadtrek manual, the battery heater comes on automatically to improve charging in cold weather. This would be useful when plugged into shore power or running the engine generator but would be counter productive with relatively low level solar charge current.

Does anyone else have similar experience? Any ideas on what causes this or how to resolve it?