I'm posting this in case it helps anyone else because I couldn't find the topic discussed here when I searched for help...
The emergency flashers (hazard lights) on my wife's 1996 2.4L Cavalier convertible stopped working, but the turn signals and all other lights worked fine. I checked the fuse box and the "STOP/HAZ" fuse was fine. (The hazard lights are on the same fuse as the brake lights.) I wasn't sure if the problem was the switch or the relay. The switch is integrated into the (~$40) turn-signal lever/module and requires removing the steering wheel and replacing the entire assembly. (There's an excellent YouTube video on how to do that from A-1 Auto.) So I thought that I'd start by replacing the relay. I have two 1996 Cav convertibles so I swapped the relays and it fixed (actually swapped) the problem. So I just ordered a ~$12 relay.
The OEM relay on my Cavaliers was located under the dashboard just to the radio-side of the the steering column. The relay is a bright-green 1.5" x 1.5" cube. (Though the replacement that I ordered is black.) On my wife's Cavalier, it was just hanging there so it was very easy to remove. On my Cavalier it was attached to to some under-dash metal with a plastic push-clip, so it was more difficult to remove. But either way, it's a pretty-easy do-it-yourself job.
FYI: In looking at relays, I learned that people who upgrade to LED lights often have problems because the relays that were designed for incandescent bulbs don't always work well with LEDs. There also seem to be relays that work with LEDs but not so well with incandescent bulbs. And there are some relays that claim to work well with both types of bulbs.