I have checked the fuses for the Hazard and the Turn Signals. Both look fine. I tried replacing the turn signal flasher (which was a task in itself). After all of this it is still not working. What else could it be? Simple short?
Maybe a simple open, but not a short, that would have caused a fuse or breaker to go. There are several possibilities including the lamps. You can't tell by looking.
Sorry I can’t give you any specific advice, I believe I have only been in an Equinox once let alone lear about there electrical system.
It should not be too bad.
Make sure all of the lamps are working, every little bulb, when you activate either a turn signal or the hazard signal. A blown lamp will prevent both the turn signal and the hazard signal from flashing. If you have a blown lamp, the other lamps will light but not flash when you either try to signal a right or left turn or lane change, or if you try to use the hazard signal. If this is what you mean when you say the lights are not working, it’s probably just one or more bad lamps.
Otherwise, what’s going on when you turn on the headlights? Do the marker lights and parking lights come on?