I might be wrong, but I don't think I am. All of the parts engines on rockauto, Advance auto, etc. don't list a 1984 F100, and I've never seen one listed anywhere/for sale. Maybe it was a Canadian/Mexican/South American thing? Plus, you've said yourself, even those books can be wrong.

We'd know for certain if we could see the vin.

If it is a 1984 F100, wouldn't the vin be F10(whatever engine code)(check digit) and the year code would be E for an 84 after those.

I think the F100 4x4's were the older trucks, not this generation. I've seen plenty of them listed on Craigslist around here. Though, they are hard to find (mainly because people turn them into redneck mobiles or just hang onto them).