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Are both indicator lights on and are they flashing?
Allegedly the Turn Signal Relay also has some connection to the Side Stand as well. The Side Stand has a switch on it so I am wondering if this Side Stand Switch is the issue. I have bo ides if the switch should be open when the stand is down or closed however if you carry out a continuity check in both postions and the reading doesn't change then I suspect this cold be the problem.
If this checks out ok then you are looking at a wiring issue or a Turn Siignal Switch issue.
I have checked this wiring diagram which is the best I can find so i hope it is right! Wiring Diagram
That looks none too pretty! I would start by repairing the wiring loom. You may have to bypass the connector if you can't get a new one! Be sure to use Heat Shrink over your solder joints to ensure a good waterproof covering.
It looks like someone has probed the wire with probe of some kind. This hsould never be doen as it allows water ingress into the wiring loom. Any testing procedures should be carried out at the connectors using back probe pins down the side of the terminal to ensure the the waterproof seal isn't damaged.
It could well be the cause. I don't know what that wire does without carrying out voltage and continuity checks however wiring should never look like that!