Nice work on the tech pix, J_C...From my broad experience, I'll narrow it to my best two guesses. It's either a stray Solid Rocket Booster jettison control module (the ULTIMATE sub-woofer system), or some sort of mid-model stereo up-grade, both lending themselves to the single-DIN chassis mount style.
By the time the '05 iteration rolled-out, the Ford Lords Of Excess had discovered this vast unexploited void of opportunity in the rt/rear wheel well, where you could stuff modules for security options, trailer "interface" co-processors, and suspension optimization. All of which I have lived merrily without, and the latter being infamous for leaving you a permanent "Low-Rider", should your friendly tow-truck driver not know about the hidden switch.
Okay, 'Nuff said about my Luddite paranoia...If the tunes sound okay as-is, it might be best not to risk invoking the wrath of those spirits that keep such things balanced. If you really want to move to the next audio level, there are several members aboard that have access to detailed schematics (and know how to use them). Even if you hand-off the job to an installer, if you ID the component (part #), and can show them a pin-out diagram source, you'll make new friends. At its most simple, a pin-out will look like "Dome Light 04, Pin 01 (red) +12V, Pin 02 (blk) -12V".
As you might guess, this component has several more plugs, and a whole buncha' more pins. Once you can determine this bunch goes to the head-unit, these must go to the speakers, and maybe these go to headphone ports. You can use something as simple as the headphone jack on an old clock radio for a signal source, and ring-out the speaker leads from this point. Multi-Gen 'Splorers are known for fatigue-failure wiring probs at the door hinges (p/windows, locks, sprkrs, etc.) I've got this thread tagged, so jump in, and I'll try to stay in touch....