AFAICT there's no setting to control that. Looking at CellBracketOptions, there's only two options for controlling the colors of brackets:
"Color" - the cell's bracket color
"HoverColor" - the cell bracket's color on mouse-over
But unfortunately, no such option like "EvaluationColor" or "QueuedColor" seems to exist.
CellPrint[Cell["Example", "Text", ...