Really tripping over my Sanberg TT4 lately to the point where I sold my Power Jazz Bass, if you have them, show them !
This one is opposite of what you’re looking for. It’s Jazz bass-shaped, but doesn’t have Jazz bass pickups.
I find this bass actually more Fender than Warwick with the painted body and bridge style with jazz pickups.
'63 Burns of London Vista Sonic - this med-scale model evolved into what was rebadged the 'Jazz Bass'. Bridge and middle pu are in the same general location as a Fender Jazz.
If by "J Bass" you mean "two single coil pickups", then I have three that aren't "really" JBs but are, sorta. First is this German-made Warwick Katana NT: Second is my Dingwall Combustion with a pair of Nordstrand Big Singles: And lastly is this (now defretted) Kiesel Icon 5 with Radium single coils.
Here's my Jazz that's not-a-jazz. It totally nails the essence of a Jazz Bass though. It's a G&L tribute neck I picked up from the TB classifieds. I modified the heel so the fretboard overhangs the body a little so it would work correctly with the Fender spec body. Hip Shot ultra light tuners, Custom Shop pickups and series V-V-T wiring (yes, series wiring that you can blend). It kills!