Question: If you find out and prove that the internal waves are “responsible”, what exactly would this mean and how would it influence science and our knowledge?

Wow kisi19chan, you did read my profile carefully!
I think you mean if they are “responsible ” of the currents at the Equator, or of currents in general, right?
Well, this would mean that we can relate the strength of the internal waves to the strength of the currents. This will help us in better understanding our climate, but also in more practical things.
For example, we know storms or tides can form internal waves. If tidal forcing decreases, and internal waves are responsible of the Equatorial currents, then also those currents will decrease. This means that there will be less heat or salt transported from one side to the other of the Atlantic or of the Pacific ocean, and this, in turn, may change the circulation of the whole ocean system (since all the oceans are connected through currents).
Changing the current system means changing, for example, where fish can be fished (and this is of extreme relevance to us humans!). Moreover, currents in the ocean have a strong influence also on our climate on land and can lead to global climate changes.
You can read more about the effects of climate change for the people here

How does climate change affect the lives of people ?

So that is why I think it’s important to understand which is the role of these kind of waves in the ocean. If we then understand them in the ocean, we can also apply the same knowledge to other fluids, like rotating stars and planet, and understand also how they works. In fact, I like my subject because it has these different aspects: on one side can help understanding our planet, but it has also what in science is called a “fundamental relevance”, that means that the mechanisms that I study can have applications in several different fields.
I hope this answers your question!