I think what bothers me the most is that the characters themselves did not bother asking or giving information about HOW to find the ship.

Where did it fly? Is it still in the area or did it go for a specific location?
Is there only one ship that looks like that or am I looking for a license plate number?
Is there a way to track it?

Nope.
Everyone just assumes it's still in the area and that somehow it will be found.

Even the excuse of the wild area which acts as a written plot convenience doesn't stand here, since it should only works if the ship is still around.