Polarization sensitivity can occur if there's something like a reflection or a half silvered mirror in the light path. I would not have expected that in an Autometer II / III, but I don't actually know the orientation of the sensor in the head of the meter. That's the reason linear polarizing filters can give odd results with cameras (like AF cameras and some others) depending on how the light is reflected to the meter cell.
If you want to test this further, try metering an unpolarized source (like a lit lampshade) through a linear polarizing filter, or a CPL filter turned backwards, and rotate the filter to see if you can measure the amount and direction of the orientation effect.
I didn't understand at first what you meant by rotating the meter 90 degrees, either, but I get it now, you mean keeping the meter input pointed at the source but rotating 90 deg around the line of sight (in aircraft terms, roll, but not yaw or pitch).