Help How to keep recirculate door closed

I would like to know how to keep the recirculate (fresh air door) closed when I shut the truck off. I shut my truck off with the recirculate light lit and the selector in vents only position. After I shut the truck off and take the key out, my truck automatically opens the recirculate door and allows fresh air into the truck. Is there a way to keep this door closed? I have a 2006 access cab.
I have researched and searched the forums before I asked and cannot find any answer.

Thank you for your help in advance

 

Why?

 

would it keep the cooler, non humid air out of the cab longer? if so, count my ass in for a mod!

 

Why? It rained really hard one day and I found water on the passenger side. Took out the cabin air filter and blower motor to find it was full of water. Researched the forum and found how the water was getting in. Made sure the "plastic shielding" next to the front windshield was installed correctly, drain holes unclogged, and installed a homemade "awning" above the fresh air vent into the cabin. It does not leak now.

However, I want to keep the door closed when the truck is off just in case my awning fails to keep the water out. Insurance purposes I guess.

 

I had a family of mice move in (twice). I was planning on screening the opening.