Do u have a night rate? In my area my day rate is .25/kWh compare to night rate .14/kWh and the time for night rate starts 9pm to 9am. All day on weekend is night rate.
You have to put a load of atleast 90watts for the pro-power onboard to stay on. This is only for 2024 or newer. It's has an option on the MMI screen to stay ON while the truck is OFF.
I have the same issue last time, i have a 2024 lariat. The dealer change the inverter, after that works fine. you need a load of at least 100watts for the outlet to be on.