Could the particle に (point in time) be in a sentence that doesn't end on a
verb? For example: 火曜日に日本語の勉強です。

If incorrect, could anyone explain why? Could it be that time-indicator に
always needs a verb?

I checked 'A dictionary of basic Japanese grammar'. All the example sentences
ended on a verb, except this one: 来年の夏（に）外国旅行をするつもりです。

(source: Makino, S. and Tsutsui, M. (2006). A dictionary of basic Japanese
grammar. 55th ed. Tokyo: Japan Times, p. 289, 290).
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question
syntax particle-に time
Particle に (point in time) without a verb
A sentence like 火曜日に日本語の勉強です does occur in everyday conversation.

> A: 来週何か予定がありますか。  
>  B: はい、月曜日にバイトがあります。それから、火曜日に日本語の勉強です。

However, it doesn’t sound quite grammatical. It sounds like something is
omitted and です is added in its place to make it sound like a proper, polite
sentence.

The casual version sounds more natural.

> A: 来週何か予定ある？  
>  B: うん、月曜日にバイト。それから、火曜日に日本語の勉強。

This sounds natural because a lot of things are omitted anyways.

When に points to a specific time, it points to a specific time at which some
event or action happens. The event or action itself may be expressed with a
noun, but you need a verb to say it happens at the referenced time.

> 火曜日に日本語の勉強が **あります** 。
>
> 火曜日に日本語の勉強を **します** 。

For this reason, a clause that ends with the time-marking に needs to modify a
verbal clause.

The sentence from your book is no exception. It should be read this way.

> ［［来年の夏（ **に** ）外国旅行を **する** ］つもり］です。

The に-clause modifies, or is part of, the verbal clause that ends with する, and
this whole thing modifies the noun つもり as a "relative" clause.
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answer