The wiring is one thing, the connections are another.
A relay is needed.
Amazon and eBay offer Fog light kits that can be installed - whether you have the correct switch or not.
The Body Control Module is where the Fog lights operate thru - you can bypass, but it might fight you. Why? You lose protection of auto turn off and auto on functions if you by-pass the BCM - it retrieves power thru the BCM for the relay coil and then uses ground from your Fog light switch - heavy lamp loads power sources are routed to the Relay at the fuse block in the engine compartment - so if the wiring is there, you're good, if not, then presume you'll have to route manually.
Headlight lamp relays are specific for each headlamp so the fog light themselves, to be switched, uses a Ground wire to ground the relay to turn on those fogs - which is powered by and thru a separate fuse - that (ground) wire needs to exist in the switches connector wiring order to make the relay work thru that switch.
Else the kits provide a separate switch you activate (throw a switch) separately.
Ford Part is
D2BZ-11654-A
Motorcraft Cross references is SW7024
If there is any in stock.
The Body Control Module powers the relay, by acting as the ground point for the coil of the relay.
IN the upper Graphic - the Fog light selection thru the switch - it grounded at the switch - which then leads back to the BCM - which in the bottom graphic, has a separate connection to the FOG Light relay. Which when the ignition is on, the Fog lights come on - and the system shuts it down once the ignition is off and the key is removed. So you know - that BCM controls many of the electrical (if not all) to save the vehicles battery.
So if you buy the switch and can't seem to get the Fog lights to work - make sure you have fuses for it installed, and it's relay, and if necessary, you can then install the fog lights but mount a switch to GROUND instead of the Body Control Module doing it for you.
This is where the "issue of the Dealerships" comes in. IF the BCM can work the fog lights because it's wired to the fuseblock, then installing it's relay is simple enough for anyone to do and the switch knob can be replaced too. To have the dealership do it, requires a considerable amount of interior work disassembly and reassembly and the actual verify and install of the wiring to the BCM from the Light switch and the inspection and rework of the BCM itself - to make that Fog light switch wire contact - GROUND at the BCM.
IF not, then the main problem you may have is that cost of them doing it, or the inconveniences of you having to do it yourself.