My best guess is it's a legit
American Vintage Reissue '62 Jazz Bass body that has been reliced and modded by it's owner.
PROS
1) the brass ground stripe to the bridge
2) the mutes holes that are unevenly drilled - these are not drilled at the factory (*)
3) the "F-19474" stamp, same as mine (2005 AVRI '62 Jazz Bass)
4) the "R" (?) written with a pencil marker same as mine (mirrored on the neck heel just opposite to it, as the ink was probably not dry when the neck was assembled to the body)
5) the holes pattern in the neck pocket (8 holes in total on mine, 6 on the OP picture, missing the 2 smaller ones)
6) one or two piece alder ?
(*) AVRI '62 Jazz Basses were
supplied with the mutes, but not installed. I guess an owner wanted to install them, was not satisfied with the resulting tone and removed them later on.
CONS
1) The bridge is non original (should be a vintage bridge with threaded barrel saddles).
2) The pickups don't have the beveled polepieces, that started AFAIK in 1998.
3) The control plate has been changed (should be with 2 stacked pots).
4) The pickguard should have an additional screw hole in the middle and the two tug bar holes (that I cannot see). There is a gap between the pickguard and the control plate.
None of the CONS above are definitive, as they may result from mods by an owner.
To be sure, one would read a bar code with a number below the shielding plate and the rubber foam in one of the pickup cavities (I believe it's the neck PU cavity).
This is the neck pocket on mine:
Even if it's not a CS body, an AVRI '62 body in what is closest to it in the Fender world.