Garry, I would be tempted to say that your vehicle may have spent a bit of time as a F1a or Loan vehicle in later stages of its life, as the two door markings represent different ownership, the square denoting HQ whereas the diamond represents 2 or B squadron, troop Platoon, battery or whatever- and the black numbers that overpaint the diamond were applied at a later time and designate something else again. (Black paint was used where camouflage was necessary and more recently, whereas the white markings were used domestically on bases where camouflage wasn't so important.) This makes me think that a number of units may have "owned" this vehicle over a time pointing to a loan vehicle that saw a number of parent units, more than likely with reserve units on exercises.
I say Reserve units , not in a derogatory way, but because in the days of S2as, reserves were mainly CMF units and only met on weekends and it makes a lot of economic sense to hold required vehicles in a pool to be used when needed, rather than allocate a large number of vehicles that may not be used on a regular basis and would deteriorate by being idle to sit at a CMF base.
Vehicles usually do not reach F1A status from new, but rather in later stages of their life when unit requirements drop, so there is every chance that the original unit may have marked it early in its life under a few consequent coats of paint.
Keep rubbing back gently and you may be lucky enough to find a common marking on both doors that may tell you more.
A Tac sign or a number on a Tac sign holder would tell you more.
Regards
Glen