> passive instrument pickup, do I need to include inductance and such of the pickup
Stuff where there is a Standard, or a Custom, you can sometimes ignore the reality of the source.
If you build a guitar amp input that looks an awful lot like 470K plus an open grid (say 100pFd), and drive it with a low-Z audio oscillator, you can compare your results to existing guitar amps tested with a low-Z source.
If you want to know what REALLY happens on stage, you better plug in a bunch of milliHenries, an on-guitar volume pot, maybe a tone pot and cap, and the 100pFd-1,000pFd of the guitar cord. And you better take account of the fact that the pickup is sorta velocity sensitive, the string is neither constant-amplitude nor constant-velocity, you have six strings all different and each string will be fretted to all different lengths....
Actually you don't design a guitar amp, you build something and play it, tweak, repeat daily for 5 to 50 years. Since others have been down this road, you can try approximating the input Z and overall gain/response of an existing design measured from a handy low-Z source, and let the pickup impedances take care of themselves. You know a guitar amp will "work" with hi-Z input, about 10mV-100mV input sensitivity for max output, a mild treble rise and optional midrange dip.
If you are going to try low-Z loading of guitar pickups, you better collect data on a LOT of pickups and onboard vol/tone circuits and figure your EQ to get the tone back to the Fender/Gibson mainstream reference.
If you have any feedback to the input device, you need to check for stability with odd reactances at the input. The canonical phono preamp is 47K||300pFd and if you do that, you can let cartridge impedance be the pickup designer's problem. But there was a large class of 2-transistor phono preamps where the feedback into the first emitter mucked-up the actual input impedance, in ways that were not obvious with low-Z drive but gave significant response errors with real pickups. OTOH there are feedback values that will motorboat badly with zero-Z drive yet be stable with the few-K resistance of most (not all) phono pickups.
Or in short: it depends. Use your brain and expect to be wrong.