Pausing the game at this point can lose you that collectible. The chief collectible, according to Lady CFII, can take a minute or two to appear after the chief points. Collectibles do not appear while the game is paused, so if you're paused during this time, you will lose it. Best to just hunt quickly and diligently during this time; you have enough time to find it, so there's no rush.
Also, this is not foolproof; often, the collectibles I'm missing are not rares; with the chief pointing things out, rares are not so rare, but there are still 48 different collectibles out there for the game to generate. I personally have most rare and commons, but I'm currently missing nine uncommon collectibles in my most advanced tribe, while I'm only missing two rare items.
Good advice about the lectures, though; I'll remember that.