When you are not connected to shore power, the red light goes on when the battery disconnect switch "Use" side is pressed, and goes off when the "Store" side is pressed. You should hear a distinct click sound when the switch is turned either way. Unfortunately, when connected to shore power, the red light is always on regardless of whether the battery disconnect is in Use or Store position.
When I first got my Airstream, I was unsure how all this worked, as you are. So I used a voltmeter across my battery terminals to double check the disconnect switch functions with shore power on. I found that my batteries showed 12.7 volts or less while the battery disconnect "Store" side was on, whereas the voltage jumped well above 13 volts when the "Use" side was on, indicating the batteries were being charged in that switch position.
These days, when I'm on shore power, and unsure of the battery disconnect status (due to the uselessness of the red light always on), I just press the "Store" side of the disconnect switch and take in on faith that my battery is no longer being charged. No problems with it after 10000 miles of use.