The only way I can think to do that without a hex pickup would only be accurate on frets 1 through 3:
Use polyphonic pitch analysis (like modern guitar tuners)
Generate +1 octave for any note below 196hz
Generate unison for 196hz and above
As of fret four, it would do three octave notes and three unison notes.
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BTW: Even if you have a Variax, or hex pickup guitar with a VG99 or GR55, it won't sound exactly like a real one. They can create the notes, but the harmonic complexity of a 12-string comes from all those frequencies vibrating together in the same guitar body.
For live use, all notes shifted works for me.
I have inexpensive acoustic and electric 12 strings for recording.