Haha - ya - we're actually busy with quotes for doing solar and batteries - but was hoping for a short term solution.Never heard of an 12V AC pump. So, the transformer is stepping down 220V to 12V. The converter you speak of is a normal inverter which would convert 12V to 220V then you use the supplied transformer with the pump as normal. Not aware of 12V DC to 12V AC inverters, that's beyond my knowledge.
I would look for a pure sine wave inverter UPS and deep cycle or lithium battery. R10k easy but then you can watch tv too. Or maybe get a 12V DC pump and charger for battery?
Now looking for a DC pump - but also need to replace the LED light as its also 12V AC. (the LED light runs on a day/night timer - so is a real pain after load shedding as it just stays off until set)
