Are the two hazard warning light relays still in place (yellow front left)? If so, you may need to trace what happened to the hazard warning light switch.
As suggested, it might be a good idea to disconnect the warning light loom from the dash. This should be via the connector on the end of a cable that comes out of the back of the dash. I would also try disconnecting the wiring harness that goes to the back of the bike. The connector for this should be under the front of the seat attached to the RH side of the BMS.
2006 F650GS in Black