Check out our Indicators QuickStart. That shows how you can use a ViewMouseDown event to see if you double-click on an indicator glyph. You could use similar logic for your scenario except don't check for double-click. When a mouse down occurs, capture the mouse and see if it starts to drag. In the mouse move event while dragging, use SyntaxEditor's hit-testing feature to see if it moves to another line.
We don't have anything built-in to do this but you can harness the mouse events and hit testing features to accomplish it.