-( Story related, cannot be missed )-
After restoring the lighthouse twice, you'll gain access to the mountain. Meeting the eccentric Doc, the mysterious Nova, and the smith Gus, you'll have in your possession only a part of the third table after Nova rushes off. Trying to use what's left of it doesn't seem to restore the tablet, though your encounter with Edmond and helping restore more buildings to bring back more citizens will give you the clue to check underwater.
Acquire the fishing pole from Cyril (the house north of Naomi/Sally in town) and buy some bait to start fishing. The goal is to deplete the stamina gauge by pressing the action button repeatedly. For myself, the first fish I caught happened to be the other part of the tablet. You'll need to try and get them pieced together, though. Doc happens to have the answer, there. Fill through his cutscenes and you'll be given your next assignment: acquiring 3 Iron Ore and 5 Glass Material. With this, he'll be able to reassemble the tablet, allowing you to power up the beacon once more.