Usually, but not always, two wh-clauses
would have a singular verb.
We need to apply both a semantic rule and a grammatical rule to the
Sentence 1 is stylistically
complicated, but can be paraphrased as
When and where [the idea] that a weary or inattentive infant
in a class must have its face smoothed downward with a hot hand
first became the conventional system.
When and where the conventional volunteer boy first beheld
such system in operation, and became inflamed with a sacred zeal
it, doesn't matter.
Now that we understand its structure, let's look
at the original version of Sentence 1, correctly punctuated:
and where it first became the conventional system that a weary or inattentive
infant in a class must have its face smoothed downward
with a hot hand, or when and where the conventional volunteer boy
first beheld such system in operation and became inflamed with a
to administer it, matters not.
Each of the two clauses introduced
by when and where can be
considered as a single unit of thought, and therefore the verb should
be the singular, is. There's a further reason for using the
singular verb. The grammatical rule decrees that with two subjects
separated by or,
the verb should be singular-except when at least one of the subjects
is a plural noun. This is not the case here. Therefore the verb should
be singular: first, because each occurrence of when and where is
seen as a single unit of thought, and second, because the two
wh- noun clauses are separated by or, which requires a
Sentences 2 and 3 do not have a grammatical rule as much as a semantic
one. The choice depends on whether the speaker or writer considers
two pairs to be a single unit, or as separate entities.
In sentence 2, the writer conceives of the ideas of when and where
to strike as a single issue and therefore uses the singular verb is.
Sentence 3 contains an ellipsis-an omission of material that might
follow when and where. Each of these ideas (e.g., when the
(imagined) love affair/ assignation might have taken place plus where it
might have taken place) is considered important in its own right
and is treated as a separate idea. This view of the ideas as separate
the plural verb were.
This is not the only possible view. The two ideas-when and where-could
just as easily be considered a single unit, and the verb could have
been was. The choice of verb number depends on the writer's
view of the ideas.
I've found a couple of similar usages in Google with how and whether:
How and whether to use such a consultation to discuss drinking is trickier.
How and whether to model other agents is a ubiquitous
issue in MAS.
In general, then, nominal clauses with pairs of wh-words
as grammatical subject take a singular verb, unless the two
viewed as separate.