Nikki, I hope I'm not stepping out of bounds here, it just seems you need some help and that's what I'm trying to do. If you read the posts by DrewE and BFL13 on page 2 of your post, the mystery switch may be explained. I said, "MAY BE" explained. It is really simple to check. Change the mystery switch from it's current position to the other position, before you do that, open the Solenoid, Relay box. Then flip the switch, if you hear a click from the solenoid or relay, you may have just found the purpose of the mystery switch. If no click, turn the ignition switch to the run position and try the switch again.
The clue is in BFL13's reply, you said there may have been a solar system that the seller removed and that switch is the one he is referring to. here is a link to how the disconnect switch works,
LINK.
The AUX switch in the stairwell is a polarity reversing switch. Its outputs go to terminals I and S on the disconnect relay. The above link explains how the latch works. In one position it causes the core to be positive and in the other its reverses the polarity of the latch coil. you know the old opposites attract, and likes attract. thats what the Aux switch does. If I'm going to far here, let me know and I'll stop but for me it's fun and gives me something to do.
Good luck, David
