Hi Diana,
Heaps of units would have used the Military District TAC plate , any unit that fell outside of a division ( 1,2,3 )or command ( Field Force, Training, and Logistic ).
So for example , Army Recruiting Sydney its unit sign would have been the red Waratah on light blue back ( as you mentioned) and a black plate with white numerals 2 over 141. DSU Watsonia would be the 3MD plate , the blue shield with the Southern Cross ( Victoria) and a Black plate with white numerals and letters, WSA over 122.
Hope you can make some sense of that ?
Cheers,
Mick