My Series II Custom has back laminates, but ... The neck laminates are visible. Mine is a replica of John Entwistle's Exploiter basses, so it's a bit different from your traditional Series II. It has a walnut core, and the birdseye maple lams sit on top of that, without covering the neck on the back or front of the instrument. And it has wood backplates, which are a must in my experience.
For me, if it has Series II electronics and other standard elements, it's a Series II. Now, if you're doing a Custom, all bets are off. I don't have one master volume, I have two, with a switch to choose between them (like Entwistle's Alembics). I don't have a pickup selector switch, I have a pan pot (which I find more useful for me than a selector switch), and an on/off switch for the LEDs. I have continuously variable Qs, which I love.
Anyway, this is a beautiful bass, Steve, and best of luck with the sale.