Well, since Paul met John while John was in the Quarrymen, then Paul brought in George, to add to that band with Colin the drummer, and one other I can recall the name of right now, I don't recall that just John and Paul were a duo for any gigs.

Even Johnny and The Moondogs and the other bands Lennon formed and named, I think the least amount of players Lennon was a part of was three, when he, George and Paul played without a drummer, until they got "tried" a drummer not Colin, then got Pete best, for his mother had a practice basement and he had a full set of drums. (rare for kids in that area to have a full set, with a nice mother making sandwiches every day for them.

So, I say, there was no duo of John and Paul after that meeting of them at that fairground event at the Wooten Village school. (I hope that's the school's name!). Didn't remember that name until I got to it in typing! Lennon either went to that school, and or that is where Paul came to hear Lennon's band.

Actually a Member Since 1996 or 97 (Number One Hundred Something).
https://www.soundclick.com/bands3/default.cfm?bandID=1409522