First of all, if this is something everyone else already knows or no one else cares about, please forgive the bandwidth.
While poking around under the couch, I discovered that the inverter (part of the boondocking option on my classic 31) had a AC power cord that was not plugged into anything. A little research found that if this plug is plugged into a shore powered AC outlet, a relay in the inverter provides the AC output from the inverter from shore power rather than the inverter circuitry. This is true whether the inverter is on or off. Prior to discovering this I was moving the AC plug on the TV back and forth between the shore power AC outlet and inverter powered AC outlet next to the TV and only turning on the inverter when I needed it. I was doing this to save wear and tear on the inverter and provide cleaner AC to the TV. The only reason I can think of why this cord was not plugged into anything in the first place is that the cord is not long enough to reach any outlets. The only outlet under the couch is the one the Converter is plugged into. I discovered this is one of the funny "one good and one plugged" single outlets. Since the cord won't reach there anyway, I bought a short heavy duty extension cord with two outlets. I plugged the converter and inverter both into this cord. Now there is no need to move the cord on the TV or turn the inverter on unless I want to watch TV on battery power. The "non-anal" approach is of course to leave the inverter all all the time. I prefer not to analyze why that doesn't appeal to me,