OP, having owned that exact model, I'll share some insights:
Like already mentioned above, that switch changes internally how each pickup works (both at the same time). You have single coil, series/humbucker, and PowerTap mode. PowerTap combines series output of a pickup (below certain x-over frequency) with single coil output (above that frequency). IMO great and very useful innovation with one caveat: since most of typical single coil hum is in high frequencies, you get most of it in PowerTap mode.
It's easy to check this yourself: If you switch back and forth from single coil to PowerTap mode, you will hear the same noise (but a little bit less with PowerTap). When pickup balance pot is in the middle, it should completely go away. If that is true, there is nothing to fix, it's the nature of this design. If I remember well, it's already well shielded.
As for your question, why you haven't noticed it earlier and now it's more noticeable, you can search this forum for "single coil noise" and read more about it, but in short: single coils do not produce that hum by themselves but are very susceptible to it. Example of source are EMI, poor grounding, ground loops, proximity to high voltage lines and so on. At my working desk, I get significant single coil noise that I can reduce if I just rotate my chair 90 degrees to my left. At one of the clubs where my band is resident, they added LED lighting around the stage last year, since then both guitar and my bass are noisy.
One more thing, again matter of opinion: I see no reason to criticize wiring of a well-made medium tier bass guitar of reputable brand, just because it "looks messy". The process of production is complex and some excess of wire (which btw doesn't interfere with any function) was surely intentional.
In short, OP you have nice bass guitar, and unless it deviates from normal functioning (like I described above) there is nothing wrong with it. Play it and enjoy it.