Yeah something is killing the battery for sure. The thing that gets me is that it is something that is not controlled by the system or it would go into battery saver mode. A test light isn't really going to help as it will always light up since the system draws a few hundred milliamps. You should use a meter and actually measure amps. One with a 10 amp capacity would work. Basically the same test except you'll be able to see how many amps whatever device it is.

Jeff