So let me see if I have this right then, When you switch the hazard switch on and the idiot light is removed all 4 indicators flash. If you turn off the hazards and turn on the ignition the indicators work ok - correct so far?
If so your last statement can't be correct - all the double pole switch is doing in effect is connecting the left and right indicators to a pulsing 12 volts coming from the hazard switch. That would have to mean there is 12 volts being switched by the relay and coming out of the "c" terminal. Put a DVM there if you have one and you should see that.
