It seems that Pairwise Dissolve does not behave the same as good old Dissolve. When polyline features that share endpoints are dissolved with Pairwise Dissolve, while they will dissolve into the same feature, they become a multi-part features even though they are contiguous.
If one wants non-contiguous multi-part polyline features they'll have to run Unsplit first? Seems to defeat the purpose of Dissolve.
From your description I believe we may have fixed this in Pro 3.2. https://support.esri.com/en-us/bug/in-arcgis-pro-the-pairwise-dissolve-tool-splits-certain-bug-00015... has a description of what we've fixed in 3.2. Does it appear to be what you are describing?
If you are able to provide an example I can try it in Pro 3.2 development version to verify your case it also taken care of.