Golly, I feel nervous about saying this but I am worried about Mark's answer. Q is not "gain". There is no "gain" in a pickup. There will be self-resonant frequency, and with inductance and capacitance in parallel, that resonance will produce a maximum response at a certain frequency.
What that frequency is, I can't measure, nor even offer an educated guess at, as my inductance meter won't register my guitar's pickup as an inductor. Without any doubt, adding the parallel capacitor will lower the resonant frequency of the combination, but I can't comment on where it will resonate before or after adding it. Adding a few hundred pF will not shift it by much. It would be swamped by the existing parasitic capacitance already present in the pickup.
It may be a matter of shifting the pickup's response away from some inner mechanical resonance, but I doubt it. You notice that Mark is careful to say that he has made an assumption. Knowing how keen manufacturers are to reduce production costs, he asks us to believe that a manufacturer would fine-tune a guitar, using ear tests. I don't buy that, it just doesn't seem likely.
When in doubt, go for the obvious answer first. In view of the prevalence of high power local AM radio stations during the production years, I'm sticking with the view that the cap is probably to shunt away radio frequency signal pickup. Knowing how easy it is for ham radio operators to be plagued by pickup in nearby audio amplifiers even nowadays, it seems a whole lot more likely as an answer.
Removing such a low value capacitor is unlikely to make the signal "brighter" - it's a hundred times too small. The effect would be too small for human ears to notice in our part of the spectrum.
I would not regard this as an issue on which any definitive answer has been given. What we need is hard facts. Since we will never know what the manufacturer was thinking, we will have to get some measurements made. Mark, what kit have you got that would help us clarify the issue?



