This van has been sitting here for months, slowly getting covered in leaves as the tyres go flat. As the rego expired last month, I finally got around to reporting it last week. When I went past a few days later, there was already an orange council sticker on it communicating an intention to tow it away. See the plastic box on the roof with beach gear in it? That's been sitting there for at least 3 months as well.
If the car has a visible rego sticker, I take a photo of that as well and email it to Council. That lets them know all the details of the car (make, model, rego and expiry date) and seems to help things along. Councils can't tow a vehicle away if the registration is current, so if you can show that the rego has expired, it makes their life easier.