Yeah that new switch Thor uses is kind of odd: It can be lit when unplugged and in "Use", when plugged in and "Use", and, more fatally, when plugged in and in "Store".
My suggestion would be to hit the button and ensure the light is on ALWAYS before plugging in--once plugged in you won't know. If you have to unplug to check do it: unplug and check.
In addition, when the battery is charging from the converter it will be higher than 12V--13V or 14V depending on the mode the charger is in.
I replaced one of my dash cigarette plugs with
a USB charger with 12V meter (Amazon). Others have replaced the plug with this
dual 12v meter (Amazon) for monitoring both house and chassis batteries.