I recently picked up the Mark King DeLuxe 12MK12959.
And now I'd like to know a little more about his past.
If anyone knows anything..... please.

Hé Sus welkom!

That would be the bass in this Showcase topic. You'll have to wait a little before Mica gets around to some serial number lookups, but from the pictures it looks like a Signature Deluxe, Balance shape (not Balance K, but the earlier Balance shape) with a gorgeous Cocobolo top and back and a continuous wood backplate.

My goodness that is pleasing to look at!

Sus, enjoy exploring the tones that can be found on an Alembic.

Here's the details I found in the file:

top: Cocobolo "Swirly"
accent: Maple laminate
body: Mahogany
back: Cocobolo "Swirly"
body shape: Balance Point
neck: 5-piece Maple and Purpleheart
scale: 34"
fingerboard: Ebony, 1.625 x 2.50 custom size
inlays: mother of pearl ovals
pickups: AXY4
controls: "Signature" volume, pan, filter x2, 2-position Q-switch x2, mono output
originally made for: Bass Central, FL
birthday: February 10, 2003

The original owner specified the custom neck size, the "swirly" Cocobolo, and the Balance Point body (as Adriaan correctly identified). It originally lived in Pennsylvania.