Like everyone else I would suspect the speed sensor. Had one go bad before and it messes with the bike big time.

 

Forget about the turn signals for now and focus on the VSS which is likely causing the speedo problem. Timing for the turn signal auto shutoff function is based on several things, one of which is the vehicles speed as determined from the VSS. Fix the VSS problem, and I'll bet your turn signal issues go away.

 

Three of the four:

1. Speedo needs the speed sensor for obvious reasons.
2. Odo need the speed sensor because its driven by counting the pulses from the speed sensor.
3. Turn signal self-cancel mechanism uses the speed sensor and an inclinometer to decide to self cancel. (That's why they won't cancel while you're sitting at a stop light, but will eventually cancel if you accidentally turn one on while driving straight.)
4... dunno why it would die at idle w/no speed sensor.

 

Cycle the hell out of the ignition switch and see if it changes anything.
Have had to take mine apart and clean it before to fix same symptoms.
Mike

 

real men don't need speedometers

 

Check the connector plug, sometimes they get water trapped inside (from pressure washing).