How do you get more island events? Or am I just at the programs mercy?

They are random, and happen only occasionally. It's typical to see them only about every 20-ish hours of game time.

I have had only 7 Island Events and I have been finished with all of the puzzles for a few days. I WANT MORE

I don't think math on that is right. It may have been what was intended but isn't what is happening. I have several games that have several hundred hours of "real" game play, never used in background. And have had 1 or 2 events and some that have had none at all. From what I have read on the forums here my experiences are not unsual. I can say I have seen more of them when on a rare occasion I leave the game settings turned on when exiting. I return to find one has occured. If the OP has had 7 events in their game, feel blessed.

A number of factors affect how often the events happen, but it's been my experience (and that of most of the people on the leader board) that the Island Events occur about every 20-30 hours. Your mileage may vary.

I agree that by sheer numbers it comes out as an average but looking at the list I also see that it fluctuates a lot. Although in taking an average you would have to throw out these two there is a huge difference between the person that got 126 events in 1339 hours and the person that had 24 in 1320 hours. I guess what I was trying to get at was I have seen in my own games that it varies quite a bit.

I'm not so sure it's wise to use the leader board as a tool for checking the practical aplication of how events should be generated. I doubt that these are what the average player is seeing. Maybe a general poll would be a better choice since that would include all styles of play as well.
Im not trying to pick on you. My goal is the same as yours really, to improve on a great game concept.