The atenach ^ is a sign of rest. In the music, it is the subdominant. The music comes to a rest at that point. In traditional plainsong, there may be a 2 beat pause.
It is rare that there is no atenach in the verse [1641/23150 in the WLC]. I have [had at this time] noted only a few places so far where they are missing and the verse is essentially one thought without pause. But I was just redoing the first secton of the Song since I had changed my technique and wanted to include the Hebrew. Because of a quirk in the music program, when I copy and paste (carefully due to other quirks), I have to re-enter by hand all the breath marks (they do not get copied).
As I was doing this, I noted that most of the verses in this first part of the Song have no atenach. The lovers are not at rest. You might be curious to know where the verse come to a rest in this love song. The music is in the usual place. Verse 1 - no rest. Verses 3 and 4 have a rest - and I have assigned them to the chorus since they all contain a first person plural. Verses 5 to 8 have a rest. Verse 9 to 17, 2.1-2 have no rest. This is very unusual. 2.3, 5, 7 have a rest.
It appears that love may be at times restless!