It's the maple cap neck. Aside from the slab body, that was the only difference. The pickup and circuit were standard. And as that tone was retained on Live At Leeds, where he was playing Frankenstein, logic points to the neck being responsible.
I used to own a replica built by @Rick's Fine '52. Maple cap neck from a Roger Waters sig, if I remember correctly. Steve Harris pickup. It had that definite extra snap and grit to the top end, so I'm content to believe the secret sauce was in the neck.