Before you start to let the parrot run you around, first get the cracker from the upper left side inside Petey's Pub.
Each time you talk to the parrot, he moves and you have to find him. He is first at the trading post. After you jump in the sea, he is on a higher window there. After you block the smoke from the pub's chimney, he is at the palm tree to the far right. After you see the pirate, he is flying above the rooftops.
After you find the pirate on the tower, you can use the cracker right there to bring the parrot over to him. Click the pirate and he will give you the map piece.
(see related question)
parrot port.
If you look at the island in the middle it is to the right of it
Parrot Port
Usually Parrot Port, for between 32 and 40 doubloons.
It is the island directly to the right of Fort Ridley, in the 3 o'clock position on the island map.
You find the navigator in the second floor of the bar at parrot port.
It's on top of the pub (on the chimney).
Parrot Port has the highest price on medicine. It is the island in the easternmost island.
Parrot Port- it is the island to the immediate right of Fort Ridley
At Parrot Port, the "vent" is the chimney on the roof of Petey's Pirate Pub.
YOURSELF! Stand on it long enough to satisfy the parrot
On top of the barrels inbetween the first house and the trading post.