I'd suggest you first get handle on the sound and general position of the harmonics in this area, then use that knowledge in the context of the piece.
The fourth-fret harmonic (which is also called the fourth harmonic) is played pretty much over the fourth fret and should sound two octaves above the note on the fourth fret (two octaves and a major third above the open-string note). Play the open string and the fourth fret first and then play the third harmonic (over the fifth fret) and the fourth harmonic (over the fourth fret). In both cases you should be playing the same notes, except the harmonics will be two octaves higher.
When you're starting with this, I suggest you try it on the bass strings first (the vibration frequency is lower and you might find it easier to produce clear-ringing harmonics) and use a pick, which has a more definite attack than the fingers. Touch the string gently above the respective frets with your left hand fingertips and lift your fingers quickly after plucking the string in order to let the harmonics ring out. When you get it right on one string, practice it on all the others.
The fifth harmonic (third fret) is more troublesome, especially since it doesn't lie exactly above the fret, but rather approx. 1/4 of the distance between the third and fourth frets higher than the third fret. It should sound an octave higher than the harmonic over the seventh fret. Again, when learning to play this harmonic start with the bass strings and use a pick. It's not easy at first, but you should get it down eventually. Once you do, move it to the other strings.
A good way to test your ability to play these high harmonics is to play the third harmonic (fifth fret), fourth harmonic (fourth fret) and fifth harmonic (between the third and fourth frets, closer to the third fret). Together, they should sound like a major arpeggio.
For bonus points, you can try to get the seventh harmonic - which lies halfway between the fifth fret and the nut, about midway between the second and third frets. The note is three octaves higher than the open string and it completes the arpeggio played with the preceeding three harmonics.
It's a difficult harmonic to play cleanly, but once you are comfortable with it, you'll have pretty much the entire useable harmonic series under your belt.