Since you know that Sidney Gigg was posted in Youghal until Feb 1910, I take it that you have his service papers which shows that? If so, they should also show his date of discharge from the RN...
I can't imagine the RN allowing its men to persue other employment while still serving. If he was living in Youghal with his family in 1911, then it seems likely that he moved there after discharge, or obtained his discharge in Ireland.
Or, perhaps, the notation 'caretaker' is wrong.
Have you found their marriage in England or Ireland, which will likely be about a year before their eldest child was born?