Jade Regent has its own subforum where GMs have talked about running the AP. Asking there might put your question in front of more eyes that have experience with it, and there might be a thread already there that will give you inspiration.
What is an intellectual encounter? Do the party and their enemies sit down and discuss their differences until they come to a mutually agreeable resolution? I had a diplomatic skald in one of my campaigns who liked to do that.
Or does it mean intellectual challenges, such as solving mysteries. I presume that by Chapter Two you mean Night of Frozen Shadows. That one has a good setup for mysteries. On the way to Kalsgard a mysterious raven watches them and then Ulfen raiders attack. Is the raven related to the raiders? The raiders, if captured and questioned, die as they are about to reveal information. Why? The party is attacked in town on many occasions, by an unknown group of ninjas. And Uksahkka's friend Ulf Gormundr has disappeared. This module is loaded with mystery.
Page 11 of Night of Frozen Shadows describes a Notoriety Point system to trigger the encounters called Events. As an experienced GM, I scrapped the NP system and arranged the encounters based on the goals of the party's secret enemies and to provide clues as the party pursued the mysteries. I described some of my changes in Amaya of Westcrown: Night of Frozen Shadows.
The Jade Regent subforum has a sticky thread (i.e., always at top of the subforum) for general questions about Night of Frozen Shadows: Frozen Shadows sticky thread.