What are these vehicles with no callsign used for?
They have Mode-S transponders / ADS-B transmitters specifically for vehicles such a the ERA SQUID, Thales MOSQUITO or Saab Sensis VeeLoPDF. 

Typically vehicles that operate on taxiways and runways are equipped with such transponders, which ensures the vehicles can be tracked by the Advanced Surface Movement Guidance and Control System (A-SMGCS).
Vehicles that only operate near parked aircraft are usually not equipped.

When using a magnetic mount, these transponders can be easily transferred between cars. This reduces the total number of transponders needed, but makes it necessary to reprogram the call sign after each transfer. For this reason it may have been decided to have no call sign in the transponder at all for these vehicles at Sydney airport.

An example of an airport using fixed installations with call signs is Amsterdam airport. Using FR24 you can see bird control, maintenance, supervisors, tugs, fire trucks etc. driving at the airport and sometimes,  when they forget to turn the system off, on the highway.



After some further investigation, I am fairly sure they use the Saab Sensis VeeLo in Sydney. The units are magnetically mounted to the vehicles. Each unit transmits using a fixed unique 24-bit address (like all Mode-S transponders /  ADS-B tranmitters) and no call sign. In the A-SMGCS software the 24-bit address is mapped to a call sign which is displayed on the Controller Working Position. There is procedure in place to ensure that when a vehicle is entering the manoeuvring area the correct mapping between the 24 bit address and the call sign is in the A-SMGCS system.