Opinions and beliefs

The question you asked is the result of modern compartmental education, it is a hindrance to The Path.

When a student becomes aware of the thinking mind and begins to detach from it

How do you detach from your thinking mind? You still have to use the "mind" to detach from the mind, isn't it? Not "detach", but observe, aware.

how the thinking mind works

It is none of your business how the thinking mind works, as how the lung, the heart... the breathe works, unless you want to be a doctor, not the "student".

Would an understanding of how the thinking mind works be an opinion and therefore lead to suffering?

Opinion formed when you hold on to your "self", then you will have like, dislike; mine, yours; good, bad... etc. If you observe, be aware, then you know; then you will be free from suffering for you are above the like/dislike but see the wholeness, literally speaking.

To start with some background, Basic Satipatthana formula is:

he dwells exertive, clearly aware, mindful,

observing ... in the ...,

removing covetousness and displeasure in regard to the world;

...

...

So he dwells observing the ... in the ... internally,

or, observing the ... in the ... externally,

or, observing the ... in the ... both internally and externally;

or, he dwells observing states that arise in the ...,

or, he dwells observing states that pass away in the ...,

or, he dwells observing states that arise and pass away in the ....

Or else, he maintains the mindfulness that "There is ...," merely for knowing and awareness.

And he dwells independent, not clinging to anything in this world.

And that, bhikshus, is how a monk dwells observing the ... in the ....

Sati’patthāna Sutta

all mental states flow along with feeling (Vedanā samosaranā sabbe dhammā)

Kiṁ Mūlaka Sutta

Now coming to your question

When a student becomes aware of the thinking mind and begins to detach from it ...

In order to be detached from your thoughts you have to remove covetousness and displeasure due to sensations created by the metal activity of thinking. So be aware of the sensations arising and passing due to mental activity as discussed in Pahāna Sutta.

Would an understanding of how the thinking mind works be an opinion and therefore lead to suffering?

What you need to understand is how sensation due to metal activity lead to covetousness and displeasure and if you abandon craving and aversion to this you come out of suffering. More on this from the Mahā Sati’patthāna Sutta:

INITIAL APPLICATION [THINKING]

Thinking of sights in the world is agreeable and pleasurable,

—and there this craving arises and establishes itself.

...

SUSTAINED APPLICATION [PONDERING]

Pondering on sights in the world is agreeable and pleasurable,

—and there this craving arises and establishes itself.

...

INITIAL APPLICATION (THINKING)

Thinking of sights in the world is agreeable and pleasurable,

—and there this craving is abandoned, there it ceases

...

SUSTAINED APPLICATION [PONDERING]

Pondering on sights in the world is agreeable and pleasurable,

—and there this craving is abandoned, there it ceases.

...

Mahā Sati’patthāna Sutta

Also see: (Kamma,vāda) Bhumija Sutta

What most people understand as opinion would in Buddhism probably be categorized under papañca (see MN18 for deeper explanation).

The knowledge that leads to letting go is something different. It has to be an immediate experience without proliferation. I like the example of the man touching a hot hotplate. If he doesn't understand that him touching the hotplate and keeping his hand there causes him suffering, then he might blame someone else for causing him suffering or form all kinds of opinions. But if he realizes that he's touching the hotplate, he automatically pulls away his hand because he understands the cause of his suffering. Likewise the Buddha said ignorance is the cause of craving and suffering.

In (Pali) Buddhism, what leads to suffering is craving & attachment rather than opinions. Opinions in themselves are not necessarily suffering. It is only attachment to opinions or opinions born of craving that are suffering. For example, the opinion that the 'sky is blue' is not suffering.