This pickup is interesting in that it's a series humbucker with each coil below only two strings. It's not often that you see a pickup with such a high unloaded resonant peak (11.6kHz) but such a low loaded resonant peak (2.7kHz). It's a great example of impedance adding, and a testament to how useless a non-loaded resonant peak is as a means of pickup comparison.
I heard lots of good things about this P bass pickup...This one seems to be the reissue of late 50s Precision, which featured that raised pole pieces under the A string, as we can see from the photo. I guess from your test that the pickup has quite a high resonant peak, even when loaded, for being it actually a humbucker for bass..!
One doubt that always concerns me especially with Fender basses pickups, Precision and Jazz Bass as well....why those couple of pole pieces (which in these "vintage style" examples are also the rod magnets, isn't it?) for every string, instead of just one pole like with guitars? How does this would translate in regards to harmonics sensing? Usually these are located under the 2 far regions of each vibrating string, instead that just under the string, like with guitars pole pieces.
I think that resonant peak of 2.7kHz is actually fairly low, and I think a series/parallel switch might be good, but then again I haven't heard of anyone doing, so maybe it's not so good.
The crazy thing is to see a pickup with 5.8 henries inductance get such a crazy high self resonant peak on account of the super low capacitance of the discrete coils in series. The way that works out still blows my mind. But it's really just a novelty, because you toss a typical 470pF capacitance on there and the 5.8 henry inductance causes the resonance to drop like a rock. It goes to show that the pickup is very cable sensitive, because the resonant peak will vary far more with cable length than will a pickup with a lower inductance and a higher capacitance.
The two pole pieces don't mean anything in terms of harmonics, because what 98% of the harmonic content is determined the location along the string, and the sensing width of the string, and this arrangement has the same sensing width as a single pole piece. It's a little more like a rail in that two pole pieces are collectively wider than one pole piece, but the harmonic difference between a rail and pole piece is small anyway (the effect of pole piece width was discussed here www.physics.princeton.edu/~mcdonald/examples/guitar.pdf). Leo Fender and a lot of other pickup makers in the 50s just tried things out on a lark not knowing if they would make a real difference. I think this two pole piece setup is an example of that.