Could be the turn signal cancel unit has been fried, the Goldwing turn signal cancel units are very sensitive to changes in the circuit and have been known to get toasted when adding after market flashers and such.
Techdude helped me out when a friend of mine toasted his when he installed a plug and play trailer wiring kit. That cancel unit has a small microprocessor that is very voltage and ground sensitive, it is located at the bottom of the steering stem, you have to pull the instrument panel to gain access to the connector, after disconnecting it you drop the assembly down thru the steering stem then reverse the process for install. The unit costs about $150.00, so you want to be sure you have cleared the fault before plugging in the new one or you will toast the new one immediately.
I am pretty sure there is a test procedure for it, I will have to look in my shop manual and get back to you on that.
Tell us if you had just finished installing something when you noticed it or did it work one day and then not the next. If t happened after installing some accessory, try disconnecting that accessory and see if they work again.