In the Kuzari (2:72), the "chaver" says of the cantillation marks (טעמי המקרא):
הם מצינים את המקום בו התכון המדבר להפסיק בין ענין לענין ואת המקום בו רצה להמשיך בענין; וכן מבדילים הם בין שאלה לתשובה ובין נושא לנשוא, בין הדברים שאמרם המדבר במהירות לדברים שאמרם במתון, ובין הצווי לבקשה
They denote pause and continuation, they separate question from answer, the beginning from the continuation of the speech, haste from hesitation, command from request
(tr. Yehuda Even Shemu'el and Hartwig Hirschfield)
The cantillation marks are usually understood as divisions and subdivisions of the words of a verse (I can give Mordechai Breuer's book on this as one example of this understanding). Apart from this passage in the Kuzari, I have never seen cantillation being interpreted as distinguishing questions from answers or commands from requests.
Yehuda Even Shemu'el notes (to 2:80) that some of the Kuzari's grammar is copied from a treatise he wrote, based on Ibn Hayyuj, but I assume that (if extant) it would have been written in Arabic. Checking the commentaries, I was directed (by Kol Yehuda) to the Akeda (gate 92, end) for illustration, but the Akeda focuses on how the cantillation stresses (מטעים) certain words by an etnach.
My question is: Does Rabbi Yehuda Halevi or anyone else explain how exactly the cantillation serves to mark questions from answers (or any of the other functions he says they serve)? And do we have any example of commentators who understood verses in this way, which would illustrate how Rabbi Yehuda Halevi understood this function of the cantillation marks?