One thing to point out: Let’s call the length of the string L, where this is measured between the active fret (the one touching the string) and the bridge. After the string is plucked with the pick, you can now touch it in various places to get harmonics [rather, kill everything that isn’t the harmonic].
(UPDATE: My rule had a bug, so I fixed it!)
If you want to divide the string into N parts, touch at L/N from the fret, or L/N from the bridge.
For example, to divide it in half, there is only one place to touch it, in the middle.
To divide it into thirds, there are two places to touch it: L/3 from the fret, or L/3 from the bridge.
To divide it into quarters, L/4 from the fret, or L/4 from the bridge.
I guess that people with great pinch harmonics put them in as they memorize the piece, but I could be wrong.
But if you have a good eye, try to aim for 1/3 or 1/4 of the string, and hopefully it will sound all Zakk Wylde!