Back to the EMS in Adelaide, I saw a short talk one of their members did on an introduction to the EMS. They are currently housed at "The Elms" at Glenside Hospital. (Co-located with the Lofty Fire Tower CFS brigade I believe)
They Operate solely on donations, which amounts to about $7000 a year (thats to pay for everything - fuel costs, property rental, medication, vehicle replacement etc).
AFAIK they are the only other registered ambulance service in SA (Other than SAAS). They are responded as others have said, by doctors, hospitals and wellfair centres. (SAAS charge $600? flat rate for treatment).
If I remember rightly, they try to keep a 24 hour service, but lack of volunteers is making it hard / impossible to do that.
There you go...