Alongside Ptolemy's two part soul runs a different association, which gives the soul to the Sun. It comes from a different intellectual lineage and it should not be blended with the first without saying so.
In the Neoplatonic and Hermetic material that grew up alongside technical astrology, the Sun is the visible image of the intelligible good, the heart of the cosmos, and the source of the light by which everything else is seen. Transferred to a nativity, the Sun becomes the ruling principle of the person: what a life is fundamentally for, and the part of it not reducible to temperament or circumstance. Later Western astrology inherited this reading, and modern popular astrology has made it dominant, which is why a person's sign now means their Sun sign and nothing else.
The two accounts answer different questions. Ptolemy is asking how a person thinks and feels, and gets two significators because thinking and feeling are two operations. The solar account is asking what a person essentially is, and gets one because that is a question with one answer or none.
The atlas records both under this entry and keeps them distinct. Treating the Sun as the soul and then applying Ptolemy's technique to it produces a reading that neither source supports, and the mixture is common enough in modern writing to be worth naming.
Sources Hermetica: The Greek Corpus Hermeticum and the Latin AsclepiusBrian P. Copenhaver with A History of Western AstrologyNicholas Campion