First, I want to say that it's a wonderful idea to help add a personal link between the PC and the story development.
And while I think Fumarole's drop-in makes sense in a thematic way, it may be difficult to explain or justify the dragon's activities and interest in current events if it's been imprisoned in the Red Pyramid's sub-subbasement for thousands of years.
Given the stated inclination for brass dragons to actively participate in humanoid social life and politics, and their emphasis on valuing independence and liberty, and this particular dragon's specific interest in Triad activity, I think it would make a lot of sense for the party to encounter it leading up to or during Book 5's slave auction at the Bhetshamtal Estate. The dragon has likely been monitoring Triad enslavement operations across Garund (including in the Mwangi) but has a hunch there's something off about the more recent events. Mekrem's missing shipment of skymetals, the head of the Jewelers Guild's capture, various artisans being smuggled into and out of the Red Pyramid...it can sense there's a larger plot, but needs to get more hands-on with the investigation.
I don't think I'd be able to resist making it a disguised guest at the event itself, someone for the party to have a conversation with during the infiltration, both suspicious of the other's intentions. Perhaps it can then quietly tail the party into the basement and then provide material aid during their rushed escape after freeing the captives. Given how freeform the heist is, you could play it out any way imaginable.
The dragon would then also be a resource of roleplay and knowledge for the party to interact with throughout the majority of Book 5, and you could decide when to make the big reveals to the summoner in question and how much help it lends to the party, or whether its trust has to be won first. Personally I would probably stretch out the ambiguity of its intentions across the full chapter, making it receptive to conversation and would offer advice but wouldn't fight or reveal itself until it had been sufficiently convinced of their righteous intentions (maybe integrate into existing influence system? Or maybe just leave as roleplay on demand.) or until there was a critical moment of dire need.