The 1980 F-series is unique as the headlamp wiring is different than 1981-1986.
Halogen Headlamps became standard in 1981, and the wiring and switch was changed to accommodate this.
The 1980 wiring is very inadequate for anything but the old standard incandescent (non-halogen) sealed beam headlights.
You can argue that the 1980-1986 headlamp wiring is inadequate, but the 1980 is even more inadequate so...
I checked the E-Bay add for the relay kit. First few things that are notable:
Battery is misspelled: "Battry"
The wiring diagram is not very detailed or accurate:
So if it was me, I'd find a different seller or relay kit just on those two things alone.
Truck: 1981 F-150 Explorer / Engine: 300-6 California MCU Feedback System / Trans: T-18 - 4 speed / 2.75 Ford Rear Axle Open Diff.