I'd suspect the harnesses are different. The HID-equipped cars have a relay mounted on the passenger-side strut tower, and the wires merge with the major harnesses in the engine compartment on their way to the lamps themselves.
The photo is the lid-off version. Item is affixed to the passenger-side strut tower, bolted-on through two holes that are bare in some models.
The car has HID headlamps. I have the wiring diagrams and shop manuals, but hadn't made an effort to discover what this thing does. (Possibly the "Fog Lamps" relays? NOPE). This is called "Auxiliary Relay Box 1", and it controls the HID headlamps. Mystery solved.
Numbers on the two plugged-in items are:
A small relay, ubiquitous among Ford models.
Inside the lid:
E-434E / E -1826C EPC
You got to figure that a factory-installed option that costs $600 or so is going to be very expensive, part-by-part. I'm afraid the alternative is aftermarket lighting, with all the attendant cautions.
ADDED: 2014 GT 5.0A conv. black: electronics, comfort, security, CA plate (FLICK U); assembled 06-13-2014, delivered 09-25-2014; odometer today (03-21-2016) 4,321.5(--> DELETED --> 2013 5.06M coupe, black:: Odo LAST day (09-25-2014) 7,975) (--> DELETED --> 2008 GT/CS: Odo LAST day (10-22-2012): 9,719.3; #2075 of 2509 convertibles, #560 of 718 in Ebony. 2009 GT/CS: Odo last day (09-08-2012): 12,000.1; #34 of 1705 coupes, #3 of 377 in Performance White. <-- DELETED <--)