Question

What could be the military advantages be for occupying an island

Answer 1

they could hid under the trees and deep into island and set up artillery to make it appear the island is deserted so when the enemy comes close to it they can open fire and the enemy will never know what hit them.

Answer 2

You are surrounded by water so it's harder to reach/ troops can't get to the island on foot, strong navy since you are surrounded by water, more isolation means less susceptible to attacks and raids, etc.