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It is located towards the right center behind the dash, to the left of the blower motor on the hvac housing:
You can access it by removing the sound insultator trim panel below the glove box.
That diagram is directly from Ford for the 2005 expedition. The parts store may have sold you the wrong part. They may have sold you the one for automatic climate control instead of manual climate control. They are different.
For automatic climate control:
For manual control(which is what you have by your description of the existing part):