Messing about on the piano as you do, I found what I believe to be the chords for Peacock Tail. All the chords are major:
G flat / D flat / A flat / E flat / B flat/F / F
That fifth chord is a B flat major over an F in the bass; on my little version it is a second inversion (ie starts on F then B flat then D) which then resolves nicely to a F major triad.
Of course, on the record it sounds about a quarter tone flat - a piano tuned to A=440Hz would sound horribly sharp.