Was it mentioned somewhere that the Blackstaff is a mantle? If so, and Eb dies, then Harry's the closest and best-prepared vessel for the mantle. So, maybe the WCouncil doesn't have a say in who gets it the staff...? Or, knowing he's going to die, Eb bestows it on Harry knowing that Harry will use it responsibly.
I don't think it's a mantle per se. WOJ is that Eb became Blackstaff sometime ca 1870, but he listed New Madrid as one of the disasters he caused with it. That's ~60 years earlier, so it seems to behave as an object he could borrow for a one-time job prior to assuming the office officially (unless NM was time travel AND mass murder, anyway).
Passing it between wizards seems like a question of who understands the burden and is willing to take it when the previous holder dies, combined with the Senior Council tolerating / trusting who has it enough not to have them beheaded. But they'd have to *really* oppose someone holding it to go for that option, because it's hard to execute one of their own to get the staff away from him without breaking it to the wider membership at large that they have an illegal wetworks man.
That's the normal scenario, though. Assuming the staff is indeed Mother Winter's, which I figure about 99.9% likely, it might well jump to the Winter knight in somewhat mantle-like fashion if he's nearby and Eb died. Which would actually be horrible, because Harry probably wouldn't be willing to cause the kind of collateral damage a Blackstaff occasionally must. Plus, Mother Winter wants it back, and he doesn't have a ton of latitude to keep stolen property from her.
