You can find the "chime" at several frets, not just 12. 7 and 19 also will chime, as will 5. The key is that the chime over any of these frets should be the same pitch as when you press the string to the same fret. 19 chime should be same pitch as 19 fret, etc.
The two tones will only be the same when the bridge in in exactly the right spot. Otherwise, the string is either too long or too short for the fixed position of the frets.
Tom Nechville recommends using 19 because slight differences in bridge placement are easier to detect at the higher pitch.