Hi - That high voice of Paul's has always intrigued me also!
I learned to sing like that just by doing it all the time, for a long time (I'm a guy). For me, it's a different voice than my speaking or talking voice, or even my "regular" singing voice, it comes from a different place in my throat (farther back?, a friend of mine who knows this kind of stuff calls it "head singing"). Funny thing is, that high voice comes from such a different part of the throat/head that it can be unnaffected even if I can have a head cold that leaves me unable to speak, much less sing with my "regular" voice!
After a while the more I listen, the more I hear that high "Paul" voice in rock harmonies. Another place that kind of voice is used (sounds almost identical to Paul when he uses this high voice) is the harmony in "Take it Easy", 2nd verse: "Standing on a corner in Winslow, Arizona", by the Eagles. Once you get the voice down, you can use it in a lot of songs.
I think Paul used this voice (the one like your "I've Just Seen a Face") really early in his singing career, it sounds like the same voice on most of "Long Tall Sally"; "Kansas City"; "Ooh My Soul"; "Lucille" and others. It then carried on with later songs of his like "I'm Down"; harmony on "I'll Get You", and "Eight Days a Week"; among others.
Addendum: VERY early on, Paul used to get laughed at with this voice, it was called a "girlie" voice, I think this was before he was even singing professionally. He was kind of copying Little Richard with that voice. I wonder if he was the first white singer to use it?
Later, when they got back from Hamburg for one of their first gigs back in Liverpool, it was that voice on "Long Tall Sally" that got Beatlemania going, the girls in the crowd just lost it with the first few notes, and that's all she wrote, according to one of his contemporaries. Sorry, no references for this, but I'll bet you can find it somewhere in the links from this site!Sorry, this isn't as helpful a post as I thought it might be. I remember asking the same question a long time ago. I think the very first thing I tried to imitate was that part in George's "Piggies" where Paul sings an ascending harmony "Eat the bacon!". It's a good practice exercise!
Hopefully "An Apple Beatle" will respond to this thread, I think he sings Paul a lot in his gigs too, I'd be very interested in his experience and explanation