Your main trouble is the nature of the electronics in a JC. The pickup is low impedance, it uses a transformer tapped at various points to make the signal up to the levels required (that's what the rotary switch is controlling) and the pots are weird values like 2.5k - you can't just stick any old pickup in there because it won't work, or at least won't work properly. Coupled with the fact that mounting pickups in a hollow body bass is a lot trickier than a solid body or even a seml-hollow bass (because you are limited to pickups which can be suspended from a pickup ring) and you will perhaps understand why you don't see a lot of JCs out there with added pickups.
I'm not saying it can't be done, but you're either going to have to source a second JC pickup (good luck with that) or some other low impedance pickup, or have completely separate electronics for the second pickup from pickup to jack, or you'd have to gut the whole bass and start from scratch. To that end, Mama pickups in Italy make a drop in replacement pickup for the JC, a traditional high impedance pickup which could be a starting point for a complete, ground up rewiring and at least mean you don't have to worry about finding something to fit the existing hole.
Good luck whatever you decide to do, but for most people, changing the bridge or tuners on a JC is as brave as they're willing to go.