As you continue your quest in Clock Tower 1F, you will encounter a quest named Watch Secret. Unlike other quest, this quest doesn't give you indicator to where to finish this quest.
This quest is located at the center of the small square inside Clock Tower 1F. You will see 3 levers at the center and you need to answer the 3 correct direction of pointers in order. The Hour Hand Adjustment, Minute Hand Adjustment and Second Hand Adjustment.
The proper orders are middle, left and right and the correct answers are VI, III, IV respectively. or BAC
The Hour Hand
The Second Hand
The Minute Hand
An NPC will appear after answering the correct pointers, and to continue, a new quest will be opened and you will need to enter the Time Rift.
You need to follow the tips to open the exit. Clicking the lever On destroys the trap.