Who/whom puzzle

The Blue Book of Grammar has a question: "John knows WHO/WHOM the winner is." The correct answer is: "John knows WHO the winner is." But ... The main clause is "John Knows." But WHOM is actually the pronoun of "the winner" and the verb "is". I used the usual rules and got 9 / 10 other questions right, but this one stumped me. Where am I going wrong?

First, we need to separate out your embedded question clause (who the winner is). That whole clause is the object of the verb knows.

Now let's look at that clause . . .

Is is a linking verb. There are no objects in linking verb clauses. You can see this quite clearly when pronouns are involved. Both the subject and subject complement are subject pronouns:

Who is he? . . . Not: *Who is him? or *Whom is he?

Here that is again as an embedded question clause (which gets inverted):

who he is . . . Not: *who him is or *whom he is

Now you can swap in the winner from your original example for he:

who the winner is

And put the clause back as your object. John knows what? Who the winner is:

John knows who the winner is.

Had you a non-linking verb instead, you would use the object pronoun whom:*

Whom does the winner like? John knows whom the winner likes. The winner likes him.

_{*Note that there are some who say that it is safe to eschew whom in any circumstance. You'll have to talk that out with your grammarian.}