The fact that the hazzards work show the circuit is ok to the indicators, the power goes from a live source that is ignition switched to the indicator unit, so check there is a live at the indicator unit, this then goes out the indicator unit to the stalk, where it stops, as it is a dead end circuit, unless the stalk is put to left or right, where current will flow to the lights on that side, this causes a bi metallic strip to heat up, as it passes the current, it gets hot and bends away from the contact so breaking the circuit, it cools bends back and touches the contact again, passes current and the lights are on again.
This is how you get the on off, so check for power at the indicator relay from ignition then power out etc.
tabetha