Mmmhh....I like this story but they finally finding the first piece necessary to achieve their dream right after MC becomes a adventurer and not before stinks...bad cliche.
If it was me I would have made they at least already had 2 gems that could not used to track the thers and the red one instead had still enough mana to resonate or the specific function to resonate.
Even that the examiner they casually invited had that information...a alternative and better way to do it would be a copule chapters with them going around hard quests and not finding a gem to show us how rare they are and the possible fake targets they gone through and after finally finding the first one being able to find the other.
Show us a room inside the castle with a continent map and every place they already had explored, a map covering fall with "x" marks almost everywhere.
Is possible they will make that a stone is on some country national treasure/crown and they had no permission to get it, the gem itself would have been a confimation that the Yamato story wasn't just a fairy tale.
