I know I'm a little late to the discussion, but I have done some research on the Fusion prior to setting ours (2019 Energi) up to flat tow.
First off, are you sure you have the 2.5 and not the 2.7? Because I'm pretty sure you can't flat tow the 2.5l. But if you have the option of the 'stay in neutral' mode, I guess it would be fine. I'd verify what you've got for sure though.
That said, I would suggest running a charge line. You probably don't need it. But, it's a highly electronic car, including the 'stay in neutral' mode (it's just an electronic rotary switch, no actual lever for shifting). I'm a bit concerned what will happen if the battery does die while towing. Since I was already running a 6 pin connector to the toad for lights, adding the power was super easy.
Also, if it's like my 2019 Fusion Energi, the 12v outlet is only active with the ignition, so I had to run a new always on 12v+ source from the engine bay into the drivers compartment for the brake system.
2004 Fleetwood Tioga 29v