The thing that bothers me about finding evidence of a lady's make up compact on a deserted island is that it's not something you would expect to find on a desert island. Bits of sea going vessels, bits from the Loran station etc...I am sure the native female population during the colonisation period would have been interested in their appearance but, an American 1930's compact on a remote part of the island?
If it did belong to AE then I would be suprised if she thought she needed to look photogenic for FN or, any other possible passers by. After all the situation was by now looking a tad gloomy. A plane that can't be flown, a missed search plane over flight, lack of drinking water, an injured navigator?those bloody crabs etc...
Still, there's no telling what goes on in a females mind and I guess Marty could be right in suggesting that AE simply might have wanted to look her best. They do seem to carry an awful lot of kit around in their handbags

Jeff