The answer came down to parts of speech. What part of speech the phrase was in a particular sentence determined whether it took hyphens. If “search and rescue” is a noun—such as “I work in search and rescue” or “I do search and rescue,” then the phrase does not need a hyphen. However, if the phrase is a compound adjective that describes a noun, such as “a search-and-rescue dog” or “a search-and-rescue mission,” then the phrase takes hyphens.
So the same words in a manuscript sometimes need hyphens and sometimes do not. When a compound adjective appears before a noun, then hyphens help readers to see that the words make up a single unit to describe the noun. For instance, in this sentence—“I have a washer-and-dryer unit in my apartment”—it’s clear that the writer is referring to one appliance; without the hyphens, the meaning is unclear. In the sentence, “I have a washer and dryer unit in my apartment,” it’s possible that there are two appliances: a washer and a dryer unit (whatever that is). Also, if “washer and dryer” are nouns in the sentence, such as “the stacked unit combines a washer and dryer,” then no hyphens are needed since the meaning is clear.
Here are other examples of phrases that will take hyphens when used as compound adjectives but will not when they appear in the sentence as nouns: