As a fan of CAN & Holger Czukay I always saw pictures of him w/the Mustang and a Jazz. I should go back and listen to the tonal differences. Maybe the earlier incarnations if CAN he was using the Mustang...? In any case I saw him live a couple of times where it was just him playing keyboards, Stratocaster, radios and a telephone solo.
From memory he only picked up the Jazz because the Mustang was stolen. It was no ordinary Mustang though!
It looks like a long channel was routed into the body, on the bass side, running from the end of the neck to the bridge. An extra section of metal tubing was added to the body to move the strap button back, further away from the rear of the bass. The front strap button was screwed into the face of the bass (a move also employed by Uli Trepte of Guru Guru), so it must be a German thing, along with wearing your bass strap over your right shoulder, ala Freddy King and Albert Collins.
Holger added a reflective pickguard at some point, having routed through the original. I've also seen some clips and photos of his Mustang with a heavy clamp or capo around the nut area, perhaps adding more break angle over the nut.
The white Jazz took over, but it is almost like his path to dumping the bass altogether was pretty set. The white Jazz had a channel routed into it, the pickguard swapped out for a green replacement, and the strap button was also moved to the front of the body though this wasn't permanent.
You can see the channel of bare wood in this photo.
If anything Holger's playing got lighter and less committed when he picked up the Jazz.