Accessory mode or Inverter for 12V cooler?

I never drive a alternator with the engine off. Shes rolling at 1200 idle when I do inverter operations.

Anything else 12 volts is generally with the engine going, since we were a team truck at the time that was not a limitation.

We did go through several alternators that year.

When the engine is off everything that is capable of drawing is also off or unplugged. Protecting the batteries is number one.