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Back when I had a 2017 F-150, I found the fuse that powered that outlet. I pulled the fuse and made a fused wire a few inches long. I used that fused wire to plug the outlet side to an always hot connection. (I put the original fuse back when I traded that F-150 in on my F-350.)
I have a 100A 12v outlet on the back of my truck, for a DC-DC charger. Not sure if it's live all the time or what (I didn't install it, but maybe it has a solenoid that turns it on/off with the ignition). But it's a good thought, I will have to check into it, and see what kind of adapter is (if) available to plug into it.
This Hennessey Takes the Expedition Tremor's Off-Roading Capability to the Next Level
Slideshow: The VelociRaptor Expedition gains a lift, upgraded suspension, Brembo brakes, and trail-ready equipment while retaining the stock 440-horsepower EcoBoost V6.