Reprogramming the AAG RS485 Weather Station

As you can see from the schematic, there are 8 Hall effect devices going to inputs to the Atmega. The data sheet identifies them as open drain switches so even though they are attached to what we might normally assume are analog inputs they must be being used as digital inputs with internal pull-ups enabled.

On the circuit board the Hall effects are arranged on about a 25mm circle with 45 degrees between them. Above them rotates the little circuit board, whose picture I've attached, that is mounted to the end of the shaft that the vane rotates. Those little gray things will just fit between two of the Hall devices or will line up over two of the devices as the shaft rotates. I presume that when a magnet is between two of the Hall devices, both are switched on.

Now, the question is, how does one compute the direction of the vane pointer? The weather station reports 1 of 16 unique positions.