In an old WordPress posting I found the property dialog image at the bottom of this post (labeled "Properties"). It was displayed for a vertical bar chart (single series).
It includes property Visible under Labels.
But in the present day (in an up-to-date version of ReportBuilder with no "About" information), in a Stacked Area chart, the Series Properties dialog appears as shown immediately below. There are many fewer properties, no "Labels" section and no "Visible" property for labels.
I can choose "Show Data Labels" and there are label properties, but again no "Visible" property.
Is a Visible property exposed "somewhere else" for a Stacked Area chart?
I'm not sure whether I should think of this more as a limitation by SSRS chart type, or more a stripping out of features in later versions of SSRS Report Builder.
I started down the path of putting an expression on more than one of the label properties to try and achieve an effect similar to "Visible", but I decided to post here before going to those lengths.
Input from somebody with SSRS insights much appreciated.