10th fret on the bottom E. The interesting thing about harmonics is that the nodes aren't
always located exactly over a fret, and the node close to the 9th fret is actually between
the 9th and 10th frets. The same area where your barring finger would be. And it's always
easier to get those 'less common' harmonics on the bass strings than the treble ones. On
the treble E the string has very little mass so you have to be very accurate to find the
harmonic at the 9th/10th fret. If you are slightly in the wrong place your fingertip damps
the vibration because the string has little energy. On the bass E there is a lot more mass
which gives the string greater energy, so if you are close enough to the harmonic node it
can still sound clearly.
Does that fit in with what you are hearing?
Another long shot worth checking is the section of string between the nut and the tuning
post. Those lengths do resonate in sympathy with the main section and contribute to the
tone of the instrument. Try strumming them with a plectrum with the guitar plugged in if
you haven't done before
E & A strings will usually sound around the pitch you are hearing. On their own they won't
sound clearly, but if they are the same pitch as the harmonic they will contribute energy
to help that harmonic sound louder and clearer.
Largely, but not entirely, dysfunctional.