TeeGrid calls OnSelect event only the first time user clicks on the same cell and this event is called after OnClick and OnMouseUp events so there is no way to detect that user has clicked the same cell twice.
First time in OnClick/OnMouseUp the previous cell is still selected and second time OnSelect is not called.

I have made a small change to TeeGrid so OnSelect is called every time the cell is selected.

Tee.Grid.Selection.pas:
procedure TGridSelection.Change change to function -
function TGridSelection.Change(const AColumn: TColumn; const ARow: Integer): boolean; // DM CHANGE
begin
  if (Column<>AColumn) or (Row<>ARow) then
  begin
    ChangeColumn(AColumn);
    DoChangeRow(ARow);

    ResetRange;
    DoChanged;
    result := true; // DM CHANGE
  end
  else result := false; // DM CHANGE
end;

Tee.Grid.RowGroup.pas: 
in function TRowGroup.Mouse line
Selected.Change(AColumn,ARow);
changed to
if not Selected.Change(AColumn,ARow) then // DM CHANGE
        if Assigned(Selected.OnChange) then
          Selected.OnChange(Selected);