Electrical 2012 GT Convertible Drain on battery - Suspect Trunk component

2012 GT Convertible
Periodically my car won't start as the battery is dead. I check the car to make sure something wasn't left on and have recently discovered that it seems to be trunk related. When issue happens I go to start car and it just whir whir whirs. I pop trunk with key fob and securely close, wait 20 mins and it fires right up. This morning I realized 2 things. Seems the interior button stuck and when I depressed it again it appeared to have released. 20 mins she fires into life in limp mode. I can always tell even if wrench isn't on because how it shifts from P to R. Its hard. I turn off car and restart and all is right.

So this morning I read about a convertible feature and that the trunk button in car is automatically disable when the top is down. I did have top down yesterday and wonder if that caused some trunk component is sticking causing the battery to drain. Any thoughts would be well received. - Thanks - Robin

Also I have a CAI and do not see any name brand on it. How can I determine it is factory ? If it is, I am wanting it replaced.

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