I would be suspicious of the bulbs you're using.
Multifunction lever at the left side of steering wheel?
see your dealer about a recall for flasher
Injector #1 output driver does not respond properly to the control signal. or Injector #2 output driver does not respond properly to the control signal. or Injector #3 output driver does not respond properly to the control signal. or Injector #4 output driver does not respond properly to the control signal. or Injector #5 output driver does not respond properly to the control signal. or Injector #6 output driver does not respond properly to the control signal.
Replace the turn signal flasher relay.
An open ground or a short to ground when the signal is on. Usually a bad bulb.
Check and make sure you have the correct bulb. The turn signal/brake light is a dual element bulb and if you have a single element it does not work properly.
signal lights not working.
Just because I had one in the past (2004 malibu) I would say that I has something to do with the fuse that works for the turn signal and brake light. Because for them both not to be working I would doubt that it was a bulb. Just my opinion. Of course you should get it looked at.
There are separate fuses for trailer signal lights in main fuse panel
No, they are not.
If signal lights fail to work when wet, first check the connections for corrosion or moisture buildup. You can use dielectric grease on the connectors to create a moisture barrier. Additionally, ensure that the housing is properly sealed to prevent water ingress. If the problem persists, consider replacing the signal lights with a more water-resistant model.
you need to change the flasher can for the signal lights