Tom, you have raised in many threads the question of how do polar explorers know when they got to the South or North Pole when compasses are ineffective. The answer is that the pole most frequently referred to as 'South' (and it's northern counterpart) is the geographic pole not the magnetic one, and as such is determined by the Earth's axis of rotation:
The Geographic South Pole is defined for most purposes as one of two points where the earth's axis of rotation intersects its surface (the other being the Geographic North Pole).
Observing the stars has always been a far more reliable way of navigation than compasses, and many long-distance sea voyages used this method for hundreds of years before GPS. This method of celestial navigation is only possible on an RE (only possible in the way it is actually done, if the world was indeed flat celestial navigation would be possible also, but the methods would be radically different due to the differing geometry of the heavens).
So there's your answer. If you are in a place where the stars overhead appear to rotate about a point directly above you, you are at one of the poles.