Date & Time: April 14th, 2022
Frequency: always
World name: Faerie
Character name: Lula Moon
Party or solo: solo
In-game time: 6:29 ET, 2:53 ST
Area and coordinates: The Howling Eye; 4.3x, 5.4y
Steps:
1. Access the Entrance for the duty Lv.44 The Howling Eye while doing the quest Lady of the Vortex in New Game+

The menu option for Duty Support that should probably say "Enter the Howling Eye with a party of NPCs" instead says "Enter the Drowned City of Skalla with a party of NPCs". Selecting that option does open the correct Duty Support window for The Howling Eye.