The flasher relay supplies/interrupts power to the switch and the switch completes the circuit to R or L blinkers, so I don't think an issue w/ the relay could be causing the problem you described, since it is located before the circuit branches @ the switch. It sounds to me like there must be a corrosion/rubbing 'bridge' (not a 'short', since that would be to ground) allowing a little current to pass from one side of the circuit to the other - I think that could only be between the switch & lights.
First place I would start is at the switch, as others said - but I'd suspect the wiring more.
Interesting mod on the led placement, kinda cool - clean off your sharpie marks though!
