John Thomas, an---------------- writer, passed away in 2018.

The correct option is eminent.

To choose the correct word to fill in the blank, let us look at the meanings of the given words and see which one fits best in the context of describing a writer:
1. Eminent: Distinguished, famous, respected, and outstanding in a particular sphere or profession. When describing a writer, "an eminent writer" means a highly respected and well-known writer.
2. Imminent: About to happen or occurring very soon (e.g., "imminent danger" or "imminent arrival"). This does not fit the context of describing a person's profession or status.
3. Prominent: Important, famous, or particularly noticeable. While "prominent" has a similar meaning, the presence of the article "an" before the blank space requires a word that starts with a vowel sound. Since "prominent" starts with a consonant sound (/p/), it is grammatically incorrect to use "an prominent".
4. Dominant: Ruling, governing, commanding, or most influential. While a writer can be influential, "dominant" is not the standard or most appropriate adjective to describe a respected writer in this context, and like "prominent", it starts with a consonant sound (/d/), which does not follow the article "an".

Since the word must begin with a vowel sound to follow "an" and must mean distinguished or respected, eminent is the correct choice.