@geofzx: I mentioned Norse navigation just because it was a fun idea, I did not think you might take me up on it!
The idea that the Norse used 'sunstones' to find the location of the sun on overcast days came from Norse sagas.
I thought this was an untested hypothesis. Fortunately if this link is accurate Viking Sunstone Navigation | The Mary Sue it sounds as if the idea has been tested. You may need to rotate the polariser and take readings at different points in the sky.
I would locate and read the paper before spending time on it though.
If you do find it works please post your solution, it would be interesting.