This was the question posed to Les Nesbitt at the September monthly meeting. Later there was some further discussion, of which see below:
When do I stop watering my Greenhoods?
The short answer is when the leaves go yellow and start to die off, usually in October- November. Allow the pot to dry out completely to dry up the roots and old tubers so that they do not go mouldy and rot the new tubers.
Australian terrestrial orchids form tubers underground. The mature plant dies back at the end of the growing season and enters a period of dormancy which for South Australian terrestrials is over summer.
A general principle of watering is to match the watering to the rainfall pattern. Whilst there is minimal rain over summer, when dormant tubers are in pots it is important to not let them stay dry for months and become desiccated. A light sprinkling every week or two is sufficient.

When do I start watering again?
For the cauline group (Diplodiums) from South-eastern Australia start watering at the end of January as the tubers are starting to shoot by then. For other greenhoods start light watering in late February and gradually increase the water until shoots appear usually in March-April. Do not let the pots dry out once leaves are visible.

Other cultivated Australian terrestrial orchids require a similar watering regime although leaves of some appear later in May or June.