The indicators and hazards share the same fuse and wiring circuit, for the hazards to work but not the indicators the fault can only be either the handlebar switch, the six pin blue loom connector or the wiring between the two.
Assuming both indicators failed at the same time that would narrow it down to a grounding fault.
There's a simplified wiring diagram here if you need one.
Open the two halves of the switch and check for continuity between the grey ground wire and the battery negative terminal.
While the two halves are open clean the switch internals:
1) Remove any corrosion on the contacts with an emery board (ask her indoors).
2) Give the internals a good dose of maintenance spray (Triple QX, GT85 or reassuringly expensive WD40) this will remove any debris left from the emery filing, any moisture and some accumulated dirt.
3) Give the internals a goodly spray of brake cleaner, again operating the switch between sprays, this will remove the maintenance spray and whatever else is left behind in the switch.
4) Pack out the switch internals with silicone grease, operate the switch to distribute the grease where you can't reach, check you haven't blocked the drain holes on the underside of the switch.
Test, reassemble, test again.