“Sitting at the king's gate”
In those days, while Mordecai was sitting at the king's gate, Bigthan and Teresh, two of the king's eunuchs who guarded the entrance, grew angry and conspired to assassinate King Xerxes. (Esther 2:21 BSB)
What it sounds like today
Mordecai just idling around by a palace doorway.
The cultural key
A modern reader pictures Mordecai loitering by a door. To the first reader, 'the king's gate' was the nerve center of the empire's business. City and palace gates were where elders judged cases, contracts were sealed, and royal administration was carried out; Boaz settles a legal matter 'in the gate' (Ruth 4:1), and Lot sits 'in the gateway of Sodom' as a man of standing (Genesis 19:1). So 'Mordecai was sitting at the king's gate' is shorthand for holding a position in the royal administration, stationed where the traffic of the court passed by. This is precisely why he is placed to overhear two of the king's own gatekeepers plotting assassination, and why the book keeps returning him to that seat. His presence there is an office, not idleness.
Recovered meaning
'Sitting at the king's gate' signals that Mordecai held an official post at the administrative heart of the palace, not that he was idling. The gate was the seat of justice and royal business, which is how he comes to overhear the plot against the king.