Perhaps the intonation on your guitar is not set up right. You should hear the harmonic when touching the string lightly at the 12th fret. Try moving your finger just a bit above and below the 12th fret, if you hear the harmonic above or below the fret, then your intonation needs to be adjusted, if that is possible on your guitar. Otherwise, you need to learn where to touch the string to get the harmonic to sound.
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