Question: Is there some sort of a pattern in the complicated trajectories of the internal waves?

Hi kisi19chan, very good question!
Yes, there are some physical constraints that internal waves have to follow while they propagate in the ocean.
These waves in fact propagate not at the surface, but along oblique trajectories, that have a specific inclination with respect to gravity (that goes vertically down, as you may know!). If you can watch youtube, look at the left hand side of this video

and you will recognize the oblique rays!
Scientists well before me figured out that this inclination changes with the frequency of the wave, and thus looking at one trajectory we can already say the wave frequency (that is, how fast the wave is going up and down). This is very important because internal waves never change their frequency, and thus, looking at the direction in which they propagate, we can understand which mechanisms formed them. For example, if they propagate at one inclination that means that their frequency is (or they go up and down) twice a day, we know that very likely they are of tidal origin, in fact tides go up and down twice a day!
But it’s important also the other way around: if you know their frequency, you can predict their direction of propagation, and thus you can also predict where they will go. In the laboratory, it is very easy to predict their behaviour, in the ocean is more difficult, because to know exactly where they go you should also know the density of the water in which they are travelling, and this information is not always available..
It is part of my job to understand these patterns and see how and why they are formed, to be able to say which are the mechanisms forcing these waves, and the property of the water they travel across.
Wow, that was an interesting question indeed, thanks for asking this!