In cases like these, it tends to be what a previous owner has done to the bike that is the cause of problems and not some inexplicable shorting of the wiring harness, although in rare cases this can happen.
As Buzz says, the hazard warning circuit has to be the prime suspect especially if the original switch is no longer there. Since the hazard warning lights are no longer functioning, the two yellow hazard warning light relays should be removed (front left) which should isolate most of this unused circuit from the bike. However, to isolate it completely, there are two diodes that would need to be removed although I'm not absolutely sure where they are
2006 F650GS in Black