If you have a multi-meter its not hard.
You mentioned two wire going to the flasher. One is power, one is ground.
Start with the side that does work. turn on the flasher, remove the bulb.
Set the meter for DC volts. touch the black lead of the meter to the bumper, or bare metal on the frame. Using the red lead try and touch the internal base socket center (Center are usually power but not always).
Be careful not to touch the side of the socket and the base simultaneously with the probe or you'll need a new fuse. Once you identified which is power (base or socket) do the same to the suspect bad light assy. If you have power on the bad side you've got a grounding issue.
Trace the ground wire back to the frame attach point. Take out the attaching screw , clean the terminal and screw w/ scotchbrite, reattach.
Barring that it could be low on blinker fluid. Sold here...
Blinker Fluid - $18.95 : KaleCoAuto.com, Your home for the rare, unusual, and hard to find auto parts.
Sorry just had to throw that in. Hope you can see that site in AU.