(noun) of (noun): subject-verb agreement

Your verb should agree with the "core" of your noun.

In your example, "train" is the core and "of thoughts" acts as a complement to train, so your verb should agree with "train". Note that as mentioned in the comments, "train of thoughts" is not exactly idiomatic, so I'll offer the reverse example to illustrate the core x complement point:

Their trains of thought were completely derailed by the recent events

in this case, "trains" is now plural and the verb agrees with it, while "of thought" remains singular, as it indicates in a way, what the train is made of, therefore, there is no need for it to be plural or even agreeing with the verb

In the case of

(A) of (B) VERB ...

Though it is typically the first noun (A) that the verb agrees with, there are cases of what the Cambridge Grammar of the English Language (p502-3) refers to as number-transparent nouns where the verb agrees with a plural (B) instead of singular (A). Consider:

A number of spots have/*has opened up.

Here the verb agrees with spots, not number.

Another example where agreement with the plural (B) is the only grammatical option would be with majority, as in:

The majority of her friends are/*is German.

Other nouns seem to be open to both options.

At the corner of Eighth and Twenty-first, a group of boys push past me. (The Haunted; Swan, Susan (Canadian novelist); 2019)

A group of boys is never up to any good. (Bound south :a novel; White, Susan Rebecca; 2009)

The list provided in CaGEL of nouns that either require the plural override or allow it are band, batch, bunch, class, couple, flock, group, herd, host, majority, minority, number, party, rash, set. Though train is not included, there are some examples to be found of the number-transparent version:

Moments later, a train of bulldozers roll down into town. (Red Man's Greed Transcript at IMSDb; https://imsdb.com/transcripts/South-Park-Red-Man's-Greed.html)

Now, take it in which of these views you please, (for there is no material difference,) and this is the whole and sole perfection, as a train of writings prove to a demonstration, which I have believed and taught for these forty years, from the year 1725 to the year 1765. (http://wesley.nnu.edu/john-wesley/a-plain-account-of-christian-perfection/)

The most popular is the Indian wedding, where a train of musicians sing, beat on drums and ring bells around the plaza. (https://travel2next.com/things-to-do-in-san-jose-ca/)

My Lords, everyone knows what a train of evils follow in the wake of overcrowding (Mr Albert York, British Parliament - House of Lords, 1898)

Of course, the writing above may be judged to be of questionable quality (or just plain dated in the last case), though they seem natural enough.

Where the plural override is used, the (B)s seem to be thought of separately, as in spots opening up one by one, boys pushing past one at a time, and people with individual German ethnicity; rather than multiple spots opening up at the same time, boys bunched together pushing past, etc.

You're looking at it wrong. This is not a string of words. And it's not "noun of noun". The of sometimes appears and sometimes doesn't; it's just extra machinery.

The important part is that this is a noun phrase, which has a structure, basically

• Determiner(s) + Adjective(s) + Noun + post-nominal modifiers

What you're calling a noun is actually a determiner, a particular kind called a Quantifier, which can be a number or a measure of quantity, like lots (which takes of), or many (which can take of the; more nuts and bolts), or quite a few (optional of the). These often have nouns in them, but it's the Determiner phrase that starts.

Determiners can come from lots of places, and quantification can be expressed in many ways, many of them metaphoric, like a train of thought, which gives you some sense of the structure.

Subject-verb agreement is not very important in Modern English. It only occurs in present tense third person singular verbs (a common verb form, but only one of twelve verb forms in English, eleven of which do not agree with their subject); and with the auxiliary be, where it's often ignored. So it's not really worth worrying about in real life. Only in school, with a teacher who has a firm grasp of singular and plural, but not much else, usually.

However, if you do want to excel at this school skill, make up your mind

• whether you're talking about one thing, with maybe several parts, like a train, or
• whether you're talking about several things, maybe connected, like thoughts.

It's up to you to decide, because only you know what you mean; everybody else has to figure it out for themselves.

Once you decide, agree accordingly.