Let's consider this
Fred Noonan was an accomplished Seaman, having been at sea all his life and rising thru the ranks to that of Captain. He was a pilot and an accomplished navigator.
Would he have hunkered down on that deserted island, knowing that the "cavalry" wasn't coming to their rescue, and just waited to die? I think not. I think thart he would have used thew materials and tools at hand to get off the island and drift, paddle, sail to the nearest occupied place (prolly Fiji) depending mostly on the winds.
Thoughts?