I don't eat because I am hungry, either. I honestly can't say I really know what hungry feels like. I eat all the time, for every reason, I'm bored, I'm stressed, I'm tired, I'm happy( celebrating), I'm lonely, I'm... you get the picture. I have never needed an excuse to eat. I think that is what is great about this diet, becuase it doesn't really limit the amount of food you can have.
Enjoy your food, and if your eating because of something else other than hunger, maybe you could find some ways to deal with that. If I'm busy, or somewhere where food is not available, then I don't even miss it. Find what works for you. Meanwhile, eat what you can have, and stick to this healthy WOE.