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I haven't figured out how to do this with styles yet but I feel as though I have made significant progress and I want to share it. Please try:

t1 = True;

Notebook[{Cell[
    CellGroupData[{Cell[
       BoxData[DynamicBox[
         ToBoxes[If[t1, Style["Open", Background -> LightRed], 
           Style["Closed", Background -> LightBlue]], StandardForm]]], "Section"], 
      Cell["Fee", "Subsection"], Cell["Fi", "Subsection"], Cell["Fo", "Subsection"],
       Cell["Fum", "Subsection"]}, Dynamic[t1]]]}] // NotebookPut