How can you determine when a phrase modifies a verb?

Take the following examples:

Until Hell freezes over, I’ll hang on to my ice-cube trays.

Although she acts truculent, Miss Hiss can be succulent.

To stuff an elephant, you need first to find out what he likes to eat.

Following the séance, Miss Hiss seemed thoughtful.

Is there a rule to help me understand what the introductory phrases modify? How do I know these phrases modify the verb in the sentence, but not the subject noun?

Try turning the sentences around.

Does it now look like it modifies I?

No, that doesn’t work. What if you try the verb?

So the clause modifies the verb.

Now look at the next example.

Which is better?

The former works, so the clause modifies the noun.

The next two also modify the noun. Do you see why?

Whenever there is a clause or any series of modifiers, you can rewrite the sentence to insert the clause or move the modifiers so that they make a more obvious reference.

Your method sounds good, but the site where I got those examples from said that all these clauses or phrases modify the main verb.

See here at the last section:

I’m not sure there is a good rule or method here, because that site (like most grade-school style grammar authorities) works from an ill-defined concept of “modification.”

Having said that, I think the idea they’re getting at with these examples is that the phrases in question tell you something about how, when, where, why (etc) the state or action denoted by the verb takes place.

How long will he hang on? Until hell freezes over.

Miss Hiss’s being succulent contrasts with what? With her being truculent. <—least convincing example alert

I need to know what an elephant likes for what purpose? To stuff an elephant.

When did Miss Hiss seem thoughtful? After the seance.

Pink frogs having a slight camoflage problem is what? It’s obvious.

I see his explanation for the fifth sentence. And looking more closely, the fourth sentence starts with a “when?” clause and “when?” normally makes an adverb so “seemed following the seance” can be read as “seemed when?”. This is a parallel to the “when?” of the first sentence’s “Until hell freezes over.” That much I understand.

I had to seek help with the others and these are the answers I found. The second sentence starts with although, which apparently makes it into an adverb clause, as demonstrated here.

And in the same way, the third sentence is a prepositional clause, which I assume he’s saying acts as an adverb modifying the verb since it answers a how? question.

So I guess either I brush up on my grammar or I don’t try to answer questions on it. I’ll do the latter and apologize for misleading you.

Do you know of a better defined concept of modification?

I’m hoping there is a better way to identify verb modifiers than the “how, when, where, why” test. Because as you point out with my second example, it doesn’t work so good all of the time.

Although she acts truculent, Miss Hiss can be succulent.

How can Miss Hiss be succulent? When can she be succulent? Where? Why can she be succulent? It doesn’t really work here.