On January 19 the Sun is unequivocally in Capricorn, making this date part of the Capricorn season rather than Aquarius. Capricorn season begins around December 22 and typically runs through January 19, while Aquarius season starts around January 20 and runs through mid-February. Because the Sun transitions between signs at specific moments each year, usually around January 20, some years January 19 could fall within minutes of the cutoff; only an exact birth chart calculated using birth time and location can confirm the sign with certainty.
This article explains the date boundary, the meaning of Sun signs, how the cusps and planetary rulers shape personality traits, and why using a birth chart is more informative than relying on a simple date list.