Indeed, Ibn Ezra the pashtan writes that it is for chizuk -- whether of the inyan or her convictions -- probably the former. Thus:
Rashi gives the famous derasha:
|Amen, amen: An acceptance of the oath: “amen” for the curse, “ amen” for the oath, “amen” whether from this man [whom her husband suspects], “amen” whether from another man, “amen” that I did not go astray while betrothed or married, while awaiting levirate marriage from my brother-in-law or after having married him. — [Sifrei Naso 1:66, Sotah 18a, b].||אמן אמן: קבלת שבועה, אמן על האלה אמן על השבועה, אמן אם מאיש זה, אמן אם מאיש אחר, אמן שלא סטיתי ארוסה ונשואה שומרת יבם וכנוסה:|
Meanwhile, Baal Haturim darshens it from a different source. This time, I agree that what he identifies as a pasek is indeed a pasek. And it stands between the two Amens. He writes that the implication of the pasek is to divide the targets of the two Amens. Amen from this man, and Amen from some other man.
Just as in my previous Baal Haturim post about Baal Haturim and gematria, I would like to posit that this is not the source of the derasha but rather an additional backup. However, I am not confident enough to say this about Baal Haturim and trup, where indeed he does seem to innovate. Indeed, perhaps he is interpreting this famous derasha, and claiming that the trup is the mechanism of that derasha. That could work.
Regardless, this is where I would differ with him. The pasek tells us nothing here.
As Wickes notes, but others as well, one very common function of Pasek is to divide between a repeated word, in the same or similar form, where the first word has a melech so that no division is present, and so a Pasek steps up to the plate. There are many such instances of this.
As such, it simply does not appear to be the case that absent the Pasek, we would think the Amen Amen applied to a single man, but the trup of Pasek is teaching this lesson. Rather, we have the repetition. The repetition causes the pasek. And the derasha is thus on the duplication, with the pasek just coming along for the ride.