How did early explorers calculate the South Pole's location so precisely?

A related question: before the days of gyro compasses, magnetic compasses were relied upon. But, the magnetic poles are not near the geographic poles-and they change position. Who kept track of the positions of the magnetic poles, so that accurate deviations could be determined?

Nobody, because knowing the location of the magnetic poles is neither necessary nor sufficient to track magnetic declination. Magnetic compasses follow the local magnetic field lines, which shift over the decades. Changes in the location of the magnetic poles are one driver of the shifts, but the relationship is not linear.

Sailors measured magnetic declination by watching their compasses on clear nights, when Polaris was visible. (After accurate timekeepers were invented, other celestial landmarks could be used.) Maps of magnetic declination were created and updated over time.

Having looked at the sun through a filter during last month’s eclipse, I can attest that, even without magnification, I would be able to work with 1/6 of its diameter if we’re talking about markings on an instrument. I was able to get decent pictures with maximum zoom on my digital camera, holding the filter over the camera lens with my other hand. This was all done freehand; with a tripod and a fitted filter on the camera, it would have been a piece of cake.