Thank you for the replies.
I investigated some more and figured out where the noise is coming from. It isn't the grill shutters (I didn't even know this vehicle had them
) or vents. It is on the air intake just past the air filter. There is some sort of mechanism in that path, and when the noise occurs I can hear that is the source, as well as feel it vibrating. Unlike what I said before, the noise appears to be periodic - about once every nine seconds.
I have uploaded a picture with an arrow pointing to the component, as well as a sound file of the click-whir occurring:
(sorry for the small image - I haven't figured out how to post a full-size link)
This occurs without starting the engine - all I have to do is briefly open the driver door and this starts occurring. It continues for several minutes (I still haven't exactly measured the time), but eventually stops.
If it's normal then I won't worry. It just seems odd to me that Ford would engineer something that cycles for such a long time with the engine cold and not running. If this is normal, I'm surprised no one else has asked about it. I searched but did not find any reference to this noise (apologizes if I did not do an adequate search).