Before jumping to any conclusions, I would check the following first,,
The way my 2009 signals work (and you are probably the same or close),, Battery positive goes to each hand control. When you push the Left turn signal switch, B+ is sent to Pin 8 of the TSM. When you push the Right turn signal switch, B+ is sent to Pin 7 of the TSM.
You Must first check to see if ANY (and I mean ANY) voltage exists on either pin when neither switch is pushed. I would disconnect the TSM connector. Turn on the ignition and see if you read ANY voltage on either pin 8 or 7 (in relationship to frame ground) when you are not pushing either the left or right turn signal switch. I bet you read something like a couple of volts on one of the pins and it is being fooled.. You don't need full 12 volts to activate a TSM logic state.
I don't have a service manual for your bike. Therefore look it up in order to double check the pins used on your year bike. They may or may not be the same. A wire from each turn signal switch goes to the TSM. Those are the wires you want to test.
If you can upload a pin out of your TSM, I can tell you step by step.