guitars

these overtones/harmonics positions also change every time you fret a string, so the vast majority of guitar playing cannot be optimized in this way. For example, if you do this for open (unfrettted) strings then the pickups will not match the wave patterns when you use frets 1-11.

By all means try moving the pickups around to see what you think sounds best, but personally I would not worry about perfectly matching the strings' wave patterns. Maybe it's worthwhile to obsess over this if you're very concerned about how open chords sound (chords that use some un-fretted strings).

you could empirically measure it by plucking a string and moving a pickup across the strings (maybe mounted on a jig above, or in a dummy body with a mechanism to move one set of pickups along a hollowed out channel; then capture the output and do a spectrum analysis showing spectral content vs pickup position.

it can be modeled as an increasing integer number of half-wavelength vibrational modes that would exist between the fret and bridge on a string, with the magnitude of each at a given position summing into your modeled output.

there are certainly effects from neighboring strings and other subtle resonance effects - I’m not a luthier so not really sure on that.