Well, an inductor (a coil) being necessary to induce some current, the measurements that I evoke are necessarily done on the coils of pickups.
The best thing to do IMHO is to measure the inductivity of a coil itself (as an air coil) then to see how its inductance changes according to the core material(s) used, leading the resonant peak to change. Here is an example that I shamelessly borrow to Dr Scott Lawing @ Zexcoil:
https://images.squarespace-cdn.com/c...g?format=1000w
If you have a DMM able to read inductance, keep in mind that it varies with frequencies and that low testing frequencies are better for guitar tranducers (any test done at high frequency being prone to give inaccurate results because of Foucault currents).
And keep in mind mutual inductance: it's normal to read a higher inductance for an humbucker as a whole than a simple addition of the inductive values of its coils separately.
EDIT - Was busy yesterday, so I can complete my answers only now.
let's say someone handed you a handful of single coil pickup poles and asked you what they were, how do you tell?
In this case and on the basis of tmy previous message: I would use a single coil with plastic bobbin (as it's the case for some Fender Strat PU's and many cheap clones) deprived of its initial magnetic poles. I would measure the inductance of its coil without poles then with various rod magnets. I'd take in account the measured weight and Gauss / Tesla of these rods. By correlating all these infos, I would have an
idea of the alloy used... but just an idea, since only lab analysis would give me a reliable answer.
That being said...
-rod magnets are meant to be A5 most of the time. For such tiny cylinders, other alloys are way less commonly used even if first Strats from the fifties had A3 and if winders have started to use other alloys (A2, A4) decades later;
-this idea doesn't help me. I'm pretty sure that a L Series Strat periodically tested here hosts PU's with A5 rod magnets when I see their inductance relatively to their DCR... but our teslameter reacts in a special way with these pickups: their magnetic field has simply not the same strength nor the same
shape (diffusion) than with modern generic A5... so, I'd have no way to reproduce these pickups faithfully when it comes to materials, anyway. I'd have to "tweak" the recipe with modern components.
FWIW.