There's an earthing problem around the indicators, I'm thinking. Maybe an idea just to trace back the wires running off the indicators and see if there's a short somewhere via a test light/probe. Safest way I know.
Double check OTHER areas, like your Flasher Unit, Turn Signal Switch could be faulty, Instrumant Lamp Rheostat may need a little check over to see if it's faulty also... I can't think of anything else... but checking all them should give you a couple of busy hours in the afternoon :P
Hope this helps