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After he ran off with the guestbook, he appears at Bangers in the Gloomy Forest, after that at the Western Island Beach. Then there's a random chance he appears at the restroom at Shiptown's harbor. Once you got that scene once, you can find him in the last cell of the bunker on Pine Island. If you're playing the public version, you'll have to wait til November 3rd for the next public update, to get the dragon's final scene.

If you found the note in Pine Island Base, he's on the 2nd floor of the town hall, you need to take the open book from the same floor to him to start the questline. (Only in patreon build at the moment 10.24.2023)