Every NPC in Quill has a birthday.
Gifting an item to an NPCs on their birthday will add a multiplier to the FP gains. To get the full benefit of this, be sure to gift a liked item. Be aware that a disliked items drop in FP will also be affected by the birthday multiplier.
Gifting an item to an NPC the same day as their birthday by chance will reveal that birthday date to you. Adding it to the calendar.
Another way to learn the dates for birthdays is to gift items and listen for any gossip relating to birthdays. When an NPCs birthday is revealed through gossip, the date is added to the calendar.
If you want to target gossip specfific for discovering birthdays, you should aim to gift items that align with an NPCs request. This allows you to pick the type of gossip you receive. Asking about "People" increases the chances of discovering birthday dates.