I'd grab my plastic safe electronic contact cleaner,
https://www.amazon.com/CRC-Industrie...df_B000RY5D0G/
And give each and every bulb socket and connector a nice cleaning. Don't forget the turn indicator lamp on the dashboard, or the connector for the Relay module, since these are part of the circuit. If reusing bulbs, make sure their terminals are clean.
The turn signal relay works by sensing current, so any additional resistance in the circuit can cause it to fail to operate. I'd make sure I had a couple of new bulbs to swap in, since any individual bulb might have changed its filament resistance over time. Not to mention, incandescent filaments aren't exactly linear resistors.
Hopefully it's not your flasher relay gone bad. These appear to be incorporated with other components on at least some model years of the GZ250, and thus are expensive to replace.
It's always good to state your model year. I see in the manual that there are different wiring diagrams for models produced for different markets as well.