Yes, this subject of pickup position vs change in sound has been discussed many, many times here deep in the archives of knowledge in Luthier's Corner.
Here are two quick pastes of mine from about 5 years ago:
About ten years back, I made up a bench mule specifically for testing out pickup position. It's much cruder that what you've built here. The body is literally a rectangle of 3/4" plywood. The neck is a partially completed leftover, not even fully carved on the back, and with pencil lines for frets. Bridge, tailpiece, pickups, neck are all just screwed down to the plywood. A small electrical panel with lab-type binding posts for quickly configuring wiring.
All the geometry is set up to match one of my Scroll Basses. And it's fitted with a used set of Chromes, which are what I use. The only pickups I tested were my own, not any standard models. I built this rig specifically to figure out where I wanted to position the pickup on the body of my Scroll Bass design.
After playing around with it for a while, my conclusions are:
Putting the pickup in the middle of the body, about the 36 fret position plus or minus an inch, gives the pickup its fullest, truest sound. That's where the pickup has the fullest range, and the flattest version of its built-in EQ curve.
From there, sliding the pickup towards the bridge basically just cuts the Bass. It doesn't turn up the Treble, but only lowers the bottom end of the curve. This is assuming that the pickup height in relation to the strings is kept the same. It's as if I had reached over to the amp and turned the Bass knob down two or three notches and changed nothing else. Not a drastic change, but a reduction in the bass end.
Sliding the pickup from the middle towards the neck, to around the 24th position, resulted in a small increase in the Bass. Like turning the amp's Bass knob up one or two notches. Again, without much effect on the Treble or Mids.
The other thing that pickup position affects is the depth of the attack curve; specifically the level of the pulse on the beginning of the note. The closer the pickup is to the neck, the louder the "pop" on the beginning of the note. But the sustained part of the note stays the same. The closer to the bridge, the lower the pop goes in relation to the sustain.
Conclusion: Adjusting the position of the pickup on the body is mostly about raising or lowering the level of the bottom end of the frequency curve, but it also affects the depth of the attack curve. Towards the neck is more percussive and heavier bass. Towards the bridge is less percussive and less bass. It's a smooth logarithmic curve in either direction. No magic sweet spots where something strange happens.
That's what I learned. I'm curious to hear what you find.
From a different thread:
Most of us established (as in grey-haired) Luthiers have gone through the process of messing with pickup positions. When I got into designing and building my own pickups about 15 years ago, like everyone else, I built a bench mule and spent some time experimenting with moving the pickup up and down the body. The results were underwhelming.
Summary:
Take one particular pickup and mount it right in the middle of the body. Set the bass Tone controls wide open, and the amp's EQ controls all on 5. That's the "natural" sound of that pickup, when used with that combination of strings, the bass frame, and the amp.
Now, if you slide the pickup toward the bridge, the change in the sound is all in the bottom end of the EQ. It's just as if you had reached over to the amp and turned the Bass knob down from 5 to 4 to 3. It's not increasing the Treble, it's moderately cutting down the Bass. That's the only thing that's changing in the overall sound of the rig.
Slide the pickup the other way, toward the neck, and you boost the Bass from 5 to 6 to 7. The Treble stays the same; the Bass end of the curve gets louder.
Sliding the pickup doesn't change whether the pickup is muddy or clear, it just subdues it or exaggerates it. If the pickup, by its internal design, is muddy in the bottom end, then sliding it toward the neck will make the muddiness louder and more obvious. Sliding it toward the bridge will make the muddiness quieter. If the pickup's natural sound is very clear and wide range, sliding it toward the neck will boost a clear bottom end. Toward the bridge, it will reduce the bottom end, but still be very clear.
The point is that most of a pickups' tonal characteristic comes from its internal construction; the size and power of the magnetic field, the geometry of the coils, the size and number of turns of wire, etc., etc. None of that changes when you slide it around on the body. All you are doing is moderately adjusting the bottom end of the overall EQ curve.
There are no real "magic sweet spots" in the pickup position. Unless your definition of Magic Sweet Spot is that "the EQ curve sounds just the way I want it right here" or "right here it sounds just like this other bass". Okay. Pickup position is pretty much a linear adjustment. You can slide the pickup where you want it to get the Treble/Bass balance of the EQ where you want it. After you've settled on one position, you can further adjust the EQ balance by reaching over to the amp and turning the Bass knob up or down.
That's what we builders and manufacturers do. We set the pickup position on the body as a final adjustment of the overall EQ balance, for that particular pickup.
