I ended up in a band that needed the P Bass sound, awkward because the only bass I owned at the time was my 1978 Jazz.
Anyhow after messing about with the sound at every gig and never being completely happy I found that setting the neck pickup at around 8 to 9 and about the same on the bridge gave me the best tone, opening the pickups fully did not work at all. If you experiment with the volumes you can plainly hear the difference around the 8/9 setting, changing the tone almost like a wah pedal, until you find the sweet spot.
I realised that what I needed was a P bass with a J width neck but all I had was an Ibanez Blazer fretless with a narrow neck, took it to rehearsal and the tone was there straight away, no faffing around, little tone change when lowering volume, tone knob working from thud to biting.
Conclusion, if you want to sound like a PBass player then you need a Pbass, you might have to find a narrow neck version a la Duck Dunn but its a Pbass you need, anything else is an approximation.
I bought a Jazz back in 1978 and stuck with it because the wide Precision neck didnt suit me, tried a Precision recently, still doesnt, but for the music I play its a Precision I need. They are plug and play always sound at least ok and are easy to control.