Hi,
Though I have lurked here from time to time in the past, I joined TalkBass today because I wanted to share some of my own experiences regarding mods to my Rick 4001.
I tried a plethora of electronic mods to this bass between 1973, when I bought it new to replace a stock Fender P, and 1985, when I settled upon how I have left it ever since.
I first chose the 4001 mainly because I liked its neck, but soon grew impatient with the hum of its single coil pickups (one of the reasons why a Fender Jazz has never been a choice of mine - the other being the narrow Jazz neck).
Initially, I added other pickups, one between the two stock Rick pickups, and another between the back one and the bridge.
There were Fender P pickups wired as they are in a Fender, DiMarzio P's, DiMarzio J's as well (because those WERE humbucking, unlike stock Jazz p'ups).
Of course, not all of those were present at once, but I did add minitoggles to allow any of the stock pickups and up to two others to be chosen individually.
I played with 'out of phase' wiring a bit, but it did not interest me much.
Something which I discovered during doing all of this was ONE of the reasons that a Rick 4001/4003 has its unique sound.
It's the capacitor in series with the back pickup, which only allows the highs and upper mids to pass thru, which when combined with the full range output of the neck pickup, yields that scooped out lower mid segment to your sound, without doing anything much yet with the tone controls of your amp, and this was introduced before many amps had graphic EQs (if any at all did) to try to emulate the frequency response of a Rick when using other basses.
An early one of my many mods was a switch to bypass that cap, thus connecting the pickup directly to the next part of the circuitry, to let the full range of the back pickup come thru, which when activated, and that pickup was used alone, made the Rick sound a lot like a Fender P to my hearing, except that the Rick had hum and the P did not.
Another part of why a Rick has its own sound is from the POSITION of its pickups along the strings.
I will suggest that the reason why the stock 4001 back pickup alone (with the capacitor bypassed) reminded me of a Fender P is because the P has its only pickup pretty close to where a Rick 4001/4003 has its back p'up along the strings, hence a similar harmonic structure is available to be captured.
The design and construction of the pickups plays a role too in defining a Rick's tonality, but IMO a lesser role than the two above factors, and same is true of the wood and strings, I feel.
It's mainly physics and math at play.
Eventually, I tired of all of the pickups which I had tried (and consequent extra switches), and wanted to simplify.
Whatever else I chose to have/keep, the stock Rick pickups would have to depart, as they had hum.
I had then-recently tried a brand new early Steinberger, and liked its sound and neck (and lack of hum), but not its price tag.
Active EMGs were Ned's choice for his instruments, and I set about getting some, a la carte.
There seemed to be a shortage at the time, but I eventually found and bought a pair, and added them to my 4001, in the spaces where my other extra pickups had been, and liked them so well that I left them there when I later removed the original 4001 p'ups.
The net result is that since 1985, I have had on my 4001 only an identical pair of EMG humbuckers, the original pickup switch, no series capacitor, one volume control (the lower resistance pot from one of the EMGs, IIRC), and only mono wiring (I had defeated the stereo feature at some previous point).
Because of the positions of the EMGs along the strings, my bass has much of the tonality of a Fender Jazz, especially if using only the back one, and some of that of a P, when both are engaged.
Since the 2 EMG pickups are identical, my back/bridge one is somewhat closer to the strings than the front/neck one, in order to more naturally maintain the balance of volume when changing choices with the pickup switch.
One point of irony which came with a very recent (thank you, Internet !) discovery by me, is that Rickenbacker HAS actually made a bass which incorporated the positioning of pickups (and likely the tonality) which I eventually achieved, but it never saw much uptake by the public.
I'm referring to their 4002 series.
Check where the pickups are located on a 4002.
It's similar to where Fender put them on their Jazz, and not far from where my EMGs have been for the last 32 years.
Cheers !