Let me walk through what I think might make the situation clearer. When we're talking about singular or plural verbs, another way of talking about this is agreement between the subject and the predicate, or even more simply, the subject and the verb of a sentence.

Anytime we have a subject which is plural, meaning there's more than one subject, we use a verb that matches or corresponds with, or indeed agrees with, that subject. So in the first example, "rain and sleet," we have two things. We thus use a plural form of the verb which happens to be “cling”: "Rain and sleet cling to the branches."

Now in the other example there's something a little tricky because the other example has "Everyday Bill or Jim" and somebody might say, well if there's Bill and then there's Jim, there are two people, so we should use a plural verb.

That would be a very logical seeming thing to think, but in this case the key is the word “or.” Every day bill OR Jim. So Bill does it but Jim doesn't. Or Jim does it but Bill doesn't. In either case there's only one person: "Every day Bill OR Jim knocks on my door." So we use the singular form of the verb, “knocks.”

So that's the general overview about the agreement of verbs with singular and plural subjects.

Now here's where things may get a little more confusing. When we're talking about nouns we usually think of nouns adding an “s” to make them plural. So one flower has no “s.” Flowers with an “s” is the plural form.

We may think this is starting to get confusing because in some cases we add an “s” and in some cases we don't add an “s.” What's going on here?

And to make things even more interesting in our examples “knock” can be both a verb or a noun. "I heard a knock on the door." Here “knock”' is a noun. "He knocks on the door." “Knock” here is a verb.

Same thing with “cling.” You have these fabric sheet manufacturers talking about the terrible evil of static “cling.” Here “cling” is a noun and of course you don't necessarily talk about, "Oh, I have so many static ‘clings' in my laundry I can't stand it!"

But if we had a plural form of the word “'cling”' as a noun it would be “clings.” And then of course “cling” is also a verb.

Okay, so now that we've thoroughly confused the situation, how do we get clarity here?

Well there's actually a very simple way to get clarity here, and the clarity comes from remembering the wider context.

The context in this case is always going to be a sentence:

In the context of a sentence how do we match the subject and the verb?

Is there one subject? If there is one subject the verb reflects that there's one subject.

Are there several subjects? If there are several subjects the verb reflects that there are several subjects.

And this is, in fact, something we do all the time instinctively. When we're talking, we don't normally confuse our verbs. We don't usually confuse that agreement between verbs and nouns unless we're learning a language for the first time. In which case it happens all the time and is very natural. Or we're talking about a particular subject that we may not be as familiar with.

So this actually gives us an insight into the study of grammar, the learning of grammar, which is that when we hone in on some topic, that topic can start to be confusing when our vision becomes narrowly focused on that topic. Of course, we have to have a focus to learn things, but the antidote to the confusion that can come from that is to look again at the larger picture. And again in this case the larger picture is the entire sentence.