Okay let me take a shot at this, you want to check post #4 for wording, did you mean in second paragraph did you mean disconnect switch Connected (battery now connected). So based on my understanding of your description I think you need to find the remote, I know you bought it used and may not have one. So you do not go crazy and/or rewire the rig I would suggest cutting power to that pictured remote controller in the basement. Some have taken the battery lead off momentarily to reset that controller which will should remove power from that black wire. Assuming that controller is functional. When reset things should go back to normal such as switches will again control devices.
Remember with these controller. once say a light is turned on via a remote it has control until you turn light off with that remote. You can throw those switches on/off till the cows come home and will have no effect, Like that security light, the controller is feeding power to that security light via that black wire, power going around that manual switch
With no shore power your converter off and your only 12VDC source to the power distribution is from the battery, when you use the disconnect switch to disconnect the battery now you have nothing powering the power distribution panel. That is why you have not lights etc.
As far as the heater, I assume you meant furnace , and when that disconnect switch connected the battery to the power distribution panel the furnace and many other devices powered from the panel will be energized, So my wild guess is the thermostat was requesting head???
This my guess based on what I thought you were describing. Keep in mind with your rewiring if you find your remote and turn on the security light that controller is going to sent power down that black wire to the that switch, ie with that switch on you will see light come on if that switch is off you will see nothing. Wiring in that switch sort of defeats the controller since it now longer has a direct shot to the a light.
If you can not find the remote or figure out how to use it , I would just disconnect power to that controller in the basement and move on.
Again this is based on my interpretation of you information. Remember I am old enough to have frequent Senior Moments. My one cent ........
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