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Chances are, Jonathan, that it came with 15s. I've never seen a 60's Ford truck with stock 14s, but then, I could eaily be wrong. Hopefully, someone else will correct me if I'm wrong!
My guess is, either way, you'll be fine, but I would recommned the 15s.
You can use any wheels that are on any F-100 thru F-150 from 1961-1996 (the 61 date, is not certain, but the bolt patterns are all the same!) The bolt pattern for Ford F-150 wheels is 5 x 5.5"
These will fit with no problem on your truck. And yes, they were 15 inch wheels.......