Hermit's Nest
Go to the top left of the island to find the hermit's nest. Speak to him and he will give you a new objective to build an archery range. The first gear is always obtained from the hermit.
Villagers Huts
Search the three abandoned huts around the island with your scout, especially inside and behind the huts. The other four gears on this island have randomized locations, but are always placed in a few specific types of locations.
Treetops
Usually, two of the gears are stashed in an area obscured by treetops, which makes them difficult to find as the island is covered in trees. Several clues tip the player off, such as a tree being separated from other trees, or colored or shaped differently.
Rock Formations
Look for a purplish glow emanating from behind rock formations, which easily stands out from the brown rock sprite. The rock formations are usually near shorelines, so you may need to circle the whole island to locate them all.