This thin, nasel-sound from Greeny's old Les Paul (middle position only, I believe) is always associated with Peter, but I'd bet he never went in search of this particular sound; it was probably more of an accident. He said in an interview once - if you take his recollections as accurate - that when he watched the Bluesbreakers perform before he ever joined, he was intrigued that Clapton always used only the bridge pickup. When Peter finally got his LP, he took this one step further and actually removed the neck pickup for a time. This probably accounts for it being put back in upside down, although I don't know how the magnet ever got flipped!
I find the tone quite close to the hollow thin sound of B.B.'s ES models, and maybe that's why Peter liked it.