Let's see, from memory:
It began life as a custom order for erstwhile Scorpions bassist Francis Buchholz in the early eighties. At a visit of his and Rudolf Schenker to
Naziville 
Nashville ze Germans did not like the original fin of the Bird (incidentally: full Korina, whether that was at Francis' request or whether they just had some korina lying around I don't know, he had been dabbling off and on with both Rev and Non-Rev TBirds in his career though he was mainly a P-Bass and later on a Warwick player). I assume that it was sunburst at the time, but did not feature the J-style yet and had different pups, possibly even pre-TB-Plus ones. This bass, with its large headstock, was probably built in advance of the Nikki Sixx-led resurgence of the TB in 87.
So the Krauts don't like it ("Vee haff ze vvvays to make you refin zis, Amerikaner!") and leave it at the factory standing in the rack and gathering dust, eventually even forget about it (because they lose another war or something or other). A young new luthier at Gibson called Phil Jones (not the amp maker) has some compassion and starts fiddling with the thing. He strips it (which was a lot of work he told me, the original fin had gone deep into the pores of the korina and korina is a pain to strip), rebuilds original 60ies TB pups from scratch and "jazzes" the neck up. (Phil Jones is today a boutique luthier und builds - you guessed it - luxury J basses, it was obviously in him already some decades back ...)
Come end of his tenure with Gibson, Jones (who designed the nineties LP bass line, the Blackbird, EB-650 and EB-750 and many others) was a master luthier there and had this Bird as his own private pet project. It was dear to him and he took it with him when he left Gibson come turn of the millenium. While he still smarts from his time with Gibson (and doesn't build boutique Gibsons today) that bass was only sold due to financial dire straits which is why it found its way to Gruhn, was discovered by Shawn/the Alembickerer who subsequently divulged his find to me ...
Der Rest ist Geschichte, thanks for listening!
PS: Funny, I never saw it as a "Jazzbird", but that is what it is! And of course the original TB IV was Gibson's early answer to the Jazz Bass (the later one was the Ripper) in more ways than one. I always found it a little surprising that Jazz Bass players don't take more kindly to the TBird and vice versa. I can't really think of any popular bass player playing both though. My like for both models is certainly related. A single coil TBird could be something too, hmmmh ...
