24 January 2017: Updated with additional information and a photo.
Steven Hyre recently posted some excellent exploded views of the F-111 wing on his Facebook page, The F-111 Historical Association. One of them reminded me that I was still hoping to find a picture of the F-111 auxiliary flap.
The production F-111B flight manual describes it in some detail. Extension and retraction were automatic but subject to limitations, e.g. it would only extend if the wings were full forward and the wing flaps were extended 28 degrees or more.
However, I had never seen any photographic evidence of it. Here are a couple of closeups of the inboard section of the wing of "Navy 6" with the flaps down.
Now it's possible that the wing in the first picture above is not fully unswept but it would appear that it is in the picture below it (note how close the wing leading edge is to the lower door of the rotating glove installation). In any event, no auxiliary flap is apparent in either one.
Posting a request for information on the F-111 Historical Association Faeebook page quickly resulted in some. Steven Hyre noted that a USAF tech instruction was issued in October 1968 to deactivate the auxiliary flap on F-111As and Cs and FB-111s, which was very early on in the F-111 program, e.g. the first production FB-111 first flew on 13 June 1968 and the first F-111C flew in July 1968 (and promptly disappeared into long-term storage). The extension limits and early deactivation explain its rare appearance in photographs.
Kevin Morrison wrote that the auxiliary flap was disconnected because it was tearing up the lower fairing seal of the fuselage opening into which the wing trailing edge swept. Bill Lassiter remembers that the lift benefit was pretty limited and there was concern that the need to first retract the auxiliary flap might delay an urgent need to sweep the wings from full forward for whatever reason.
And best of all, Patrick Flohe provided the following closeup of the auxiliary flap lowered on an F-111A.
He also noted that at the time the photo was taken, this airplane still had the original aft main landing gear door that opened parallel to the bottom of the fuselage.