If you were standing on the South Pole at the time of the autumnal equinox, where would you expect the Sun to be at midday?

When the earth experiences the Spring or Autumnal Equinox, the sun is exactly above the equator. This means that the two hemispheres receive equal light, for example.
If the South Pole is at a 90 degree angle with the equator, and the sun is in line with the equator, then it would be correct to say that the sun will be positioned exactly upon the horizon. The sun would appear as a half circle bisected by the horizon line.
To say midday in reference to the South Pole is a bit strange. The South Pole is in every time zone simultaneously, and would therefore have no proper time. Instead, you would say that this even occurs exactly on the equinox, which is the moment the sun aligns with the equator. This is a time, not a day, and could be calculated exactly.