If your turn signals are doing strange things then the your first assumption is probably that the flasher relay has gone bad. This is a logical assumption but on K bikes this usually is not the case as the flasher relays are generally not prone to failure. There are a couple of things to check before replacing the flasher relay.
1 Check the fuses: The flasher relay has both switched (Fuse 7) and unswitched (Fuse 3) power. If it is not getting power from both of these then it can exhibit erratic behavior. Note that K bike fuses can appear to be good when they're not so it's advisable to test their continuity as opposed to just visually inspecting them.
2. Clean out the starter motor: Parts of the electrical system are grounded through the starter motor. When crud builds up over time inside of the starter this ground connection can become flaky and cause electrical gremlins.
In case you're interested, here's the flasher relay pinout:
(http://i278.photobucket.com/albums/kk91/electro_handyman/Bike%20Tech/flasher_relay_pinout.jpg)
(Note that the auto turn signal cancel feature can be disabled by cutting the blue/green wire.)
edit by scott_ 10-12-13 to update missing photo's