Electrical conductivity detectors are standard fare in laboratories, namely in gas-liquid chromatographs. There are numerous manufacturers; although, I am not sure what would be available in Australia. But in my experience, the circuits for the detectors were available in the service manuals and are simple. Typically, the gas jet is one electrode and a small cylinder above or in the flame is the other electrode. They are quite sensitive to impurities in the flame, hence their use as detectors in chromatographs. However, since you are interested in basically and on/off application, that should not be a major problem. Instability of the flame might be a problem, as it would be with anything that did not have a large thermal mass; however, various damping techniques and positioning of the electrode(s) should be able to address that problem.
A different alternative would be to look at the spectrum of the flame. For example, the emission spectrum (or absorption spectrum) should be quite different than the background thermal emissions. For leads on that method, I suggest looking into atomic absorption or atomic emission spectroscopy. Both of those methods would be more complex than simple electrical conductivity.
And last, one might monitor CO2, CO, or H20 production, or unburned fuel gas by IR absorption or other specific methods, including simple mass spec. Again, the flame would produce those gases, but the background heat might not, unless of course, one were monitoring near the molten metal. John