Top to bottom, the controls appear to be labelled, Volume, Balance, Treble/Bass and Midrange. Of these, only the first and last could possibly be push-pull pots.
It is perfectly possible that no series/parallel or coil splitting options are offered. Arguably, the whole point of the dual J pickup is noise-cancellation and, perhaps, a pseudo-Stingray sound.
Of course, it would be a simple task to add mode switching.
Right on. I figured there would be some sort of splitting available. I cant wait to get my hands on it! I will know more next week.
The "classic" MusicMan Stingray Bass features no coil switching. (By comparison, some of Leo Fender's designs for G&L positively bristle with mode switches.) Some EBMM models feature a blade switch to select coil combinations.
One idea that might prove interesting on the American Deluxe Fender is a series/parallel mode switch for the JJ pickup.
For the most part, I agree that you would be wise to leave the instrument stock. Some of the tonal variation that might come from pickup mode switching should be obtainable from 3-band active EQ.
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You mention a Jazz Bass. Is this Standard in the Made In Mexico sense or "standard" in the sense of single coil pickups and passive control electronics?
If you are content with the playability of the bass guitar that you already own, it should cost far less to upgrade its pickups and control circuitry than to purchase another instrument.
You might try rigging it up for a split where the half of the P and one of the Js are in series. Maybe run the two coils of the P to a Blend control: center is both coils, up or down is one or the other. When using them with the double-J (or even a split J), you can tweak the P in or out, up or down. Might hit upon a unique tone.
If you like the way the instrument plays, the way it sounds, the way it looks and the asking price, go ahead and buy it.
As for versatility, there are times when less is more. Fewer options can mean less time wasted, fiddling about, trying to arrive at the right control settings.
I can imagine using the P sound. I can imagine using the dual J sound. I am not so certain how usable the in between sounds would be. If you find yourself only using the two extremes of the Balance pot, there would be a case for converting to a selector switch.