Just saw this post and read through the comments above. This is a new one for me. My first reaction was, what does the battery 12 volt system have to do with the AC 120 volt system? The common junction point is the converter (breaker panel).
The battery kill switch will shut the battery off. But if you are still plugged into shore power, the battery is now in a disconnect mode (same as disconnecting it) and all your house lights are now running through the converter's 12 volt DC output. House lights are 12 volt DC as is the furnace.
For anything AC powered, like the microwave, the common point of contact is the converter.
If the house lights are turned off, I don't understand how they can flip on all by themselves. But, this is what you are experiencing.
Easy test. Flip the battery kill switch. Unplug shore power. Everything should be powered off. Check everything. If you have an inverter, flip the kill switch to it also. On my 5er, the inverter is wired separate, on it's own kill switch and fuse system, directly to the battery. I does not have any dependency on the "converter". Everything off? Double check every plug and every light.
Now flip house battery on (leave "inverter") off. Turn on furnace (battery only), and let it cycle. Do house lights (12 volt battery) come on? If so, the common junction is the converter. If not, do just the opposite.
Kill the battery (disconnect or kill switch). Plug into shore power now. Converter will power your 12 volt system and your 120 volt AC system. Turn furnace back on. When it shuts off, do house lights come on? If so, the common junction point is the converter (breaker panel).
One more test. Unplug from shore power. Kill switch or unhook battery. But turn on and power up the inverter. What systems are now running? House lights and microwave? or just the refrigerator? Does the furnace run with just the inverter turned on.
Why do the three separate power feeds? To eliminate the inverter that's it back-feeding somehow into the converter, probably through the transfer switch that toggles the power outlet from the inverter, switching power from Shore power (AC 120) and the inverted battery to (AC 120), which is now powering the Converter (breaker box).
This will eliminate or confirm the problem is with your inverter. Anything, it's something to think about.
