Across (covering all area/part of)

Example sentence:

Harry moved his head over on the pillow. In the bed to his right lay Hermione. Moonlight was falling across her bed.

My research:

According to various dictionaries, the definition of "across" varies:

1. Covering whole area of something.
2. Covering parts (but not whole) of area.

Is there any rule to figure which definition should be used in what context, for example in this context?

There are two usages of across in play here. Cambridge Dictionary starts out with most direct and simplest definition: "from one side to the other." Note that this says nothing about covering something, but about, well, crossing it. It talks about direction and completion, not about square footage. (In geometry terms, we're talking about a vector with this definition).

At first I forgot about the other usage, and was going to write an answer saying "across doesn't imply anything about coverage." But then I came across the helpful sentence lower in Cambridge's entry: "If something is happening across the country, it is happening in all parts of the country." If I "drive across the country," I certainly don't cover all of it, but if I "spread fear across the country," the understanding is that my effects are widespread.

This meaning is causing you confusion. But I think Merriam-Webster helps narrow it down: their definition for this usage is to equate it to "throughout." This usage doesn't equate to "covering," because "covering" carries too specific of a prepositional intent, communicating that X is "on top of" surface Y. I suggest that you replace "covering" in this definition with Webster's suggestion of "throughout," with the sense of "permeating." To adopt Edwin's illustration, a bridge can't stand throughout the river, and moonlight can't fall throughout a bed.

So where is the "rule to figure which definition should be used in what context"? As is often the case with contextualization, it is less a rule and more an exercise in common sense, but there is a key point. The two usages alter the meaning of the verb; the difference between the two is in whether the verb (and maybe somebody can help me out with the terminology here) has a "quasi-transitive" or "quasi-intransitive"* relationship with the object of "across." What the heck do I mean? Consider:

• The boat rowed across the river. The boat did something "to" the river, in relation to the river.
• Rejoicing broke out across the country. Rejoicing just happened, "quasi-intransitively," and the country is simply a location.
• A bird flew across the street. The bird's flight is directionally related to the street.
• Flags flew across the country. Flags flew—that is, "were flown," an intransitive use of to fly.
• Fireworks flew across the city. This one... could be ambiguous, and be taken either way. Either "throughout the city, fireworks were flying," or some whizz-bang rockets made it all the way from city limits to city limits.

In the Harry Potter example, even if it were possible to take a "moonlight fell throughout the bed" reading, it would subtly change the meaning of fall. Whatever this kind of "falling" is, it's not something that happens "to" the bed, just something that happens, and the bed just happens to be the place where it does. This of course is not how "moonlight falls."

So the "rule" you're looking for is: Does the context suggest that the verb has a transitive relationship with the object of "across"? If so, it's the "from one side to the other" definition; if not, the "throughout" definition.