Identical flageolet notes

[Mike_Kinny]

Hi everyone,

Wondering why everybody plays the flageolet on 19th fret instead of the more convenient 7th fret.

William Walton Bagatelle No 3

[Gitfiddlemann]

I'm guessing it is primarily for tonal color purposes. They are the same note, but don't quite sound the same, because of string length. The harmonic at the 19th to my ears is a little more staccato like, a bit more percussive, which fits better with the overall phrasing and tonal goal of the passage imo.
Plus, it's a natural extension of the RH fingering, at least the way she does it. Seems smooth, and just as easy to execute, leaving the LH alone to take care of the fretted notes.
(Incidentally, it's the first time I hear the word "flageolet" used to describe harmonics on the guitar. My ignorance I guess. )

[cotten]

Being a recorder player, when I see the word "flageolet" I think of an actual flageolet. https://en.wikipedia.org/wiki/Flageolet

cotten

[rick-slo]

The 19th fret is right there for both the right and left hands (economy of motion, and one can even maintain legato on some other notes if indicated). Most fingering is worked out to minimize chances of making playing errors, although, as Andre pointed out, tonal considerations also play a role.