Island Events occur only about once a day under ideal conditions, and may be far less frequent than that. If you don't open the game for a long time, you will only get one when you do turn it on again. They don't "stack up" while the game is off, and it's not unusual to go for several days without seeing one.

I'm not sure that I understand why you are avoiding the graveyard puzzle, though.
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Barbara
Unicorn
Last Day of Work