What is the name of this kind of vertical separator between sections? I've seen it somewhere but can't remember where or what it's called. It's likely a specific type of printer's ornament, however I can't seem to match it anywhere.
Many visual items or styles don't have any specific name. Often objects/style are merely discerned by a description or they fall under some blanket term(s).
In this case, the image posted is simply a filigree, ornament, decorative element, flourish, chapter marker, etc. There is no particular name solely based upon how the element is constructed or because it may be used commonly in some settings.
For example a "Johnson Box" is a specific term for an item, but that name has nothing to do with how the item appears. The name is based upon usage. This is similar to your sample image - any name is based upon usage. There's no name based upon appearance.