Level datums have beginning and end extents. This means they will only appear in views which include a part of their length. See the first image below. To pull the level's start or end so it appears in your new section view, then activate your new section view. Then, first, toggle the view setting to Do Not Crop View (red number 1 in image). Second, click whichever end of the level is nearest your new section view's borders, then drag the level end over so it is within your new section view's crop region (for best results, ensure your section view's crop region is visible). All levels locked to that level should drag with it. Then you can toggle the view setting to Crop View and the dragged levels should be visible.
To toggle a Level bubble to be visible or invisible, simply click the level's datum line, then click the check box which appears off to the side a little ways. See the image below. Also, just so you use correct lingo, the level's bubbles are not Tags, they are called "bubbles". This is to distinguish that they are not related to Revit's Tag functions.
