Leonardo da vinci's notebook is on the high ledge to the left of the Statue of Liberty. Climb up to the top and jump left to reach it. Return it to 1516 AD.
it is in time tangled island in 1882!
It isn't on the island. The Statue of Liberty is, but it is still in France in 1882 AD.
The special sunglasses from Spy Island were an item on Time Tangled Island, but are no longer there.
There is no paint brush as an item on Time Tangled Island. There is at least one in the scene at the workshop of Leonardo Da Vinci (1516 AD).
There is a "shack" on Shark Tooth Island, by the beach. There is a "construction shack" at the bottom of the Statue of Liberty on Time Tangled Island (1882 AD).
The construction of the Statue of Liberty is taking place at 1882 AD (10 o'clock on the time device).
If you "beat" the island, then the glider (a reward for returning the notebook) is already in your item bag.
The special "spy chic" sunglasses were once a special item on Time Tangled Island as a promotion for Spy Island. They are no longer in the designated location there. All of the Headquarters agents on Spy Island are wearing them. (see related question)
The Mission Printout is selected as the first item in the Lab on Time Tangled Island. It does not provide any real information, only tells you that items are out of place in time and you have to go to the future to find out more.
The oracle is in the building on the hill on Time Tangled Island.
Frederic Bartholdi (1834-1904) was the designer of the Statue of Liberty. On Time Tangled Island, he is at the statue in 1882 AD. Go right and enter the construction shed to return the study model of the Statue (from the top of Mount Everest in 1953 AD).
There are no horses, winged or otherwise, on Time Tangled Island.