Flashers will work when the "red triangle" is pushed but I get intermittent use on the blinkers for turns. Flick the lever and left or right may or may not work. If they don't work then both do not work, not just one.
Do the thing where you push in the red triangle and hold it for a while - this gets it going for a while but not long.
Replace the flasher??

 

I am having the same problem and have been advised that I need to replace the hazzard switch which controls the turn signal flashing. I have been looking at a device that apparently bypasses the hazzard switch with a flasher dedicated to the turn signals and mounts under the steering column thereby avoiding having to remove a lot of components from the dash to reach the faulty hazzard switch. Sounds good but I would like to hear from anyone who has used the bypass and then I assume the hazzards themselves would not be fixed if you used the bypass. Sorry did not mean to hijack your thread.

 

Hi Irish Whiskey, how is that buddy of yours who looked at a C5 for me last year?

I had the same problem as you, exactly the same. I ended up buying the switch (not from a stealership) and replaced it over the winter. I used a DIY thread as a guide and it took less than 1 hour. I think I paid $39 for the switch. If you want the link to the DIY, let me know and I will put it up.