Cutoff switches and fuses are for safety. To isolate the load.
I went this route. Relay under the hood with control side tied to the OEM AUX switches in the front cabin panel. 500 amp fuse as close to the battery as I could get it.
That is the cooling fan on the inverter kicking in because you have enough of a load to get it warm. Congratulations on using the inverter as advertised by Toyota. Not many will do so.
On long drives, it can be really annoying. I have to lower the cabin temperature to get it to quit.
When...
With this setting ON, if the digital rear view mirror thinks something say, a garage door or a towel, is blocking its way it automagically switches to optical mode. Call it "Auto optical" if you will.