I have a 2001 Miata. Signal lights work fine when headlights are off. They don't work when they are on. The left signal indicator on the dash is just always on but doesn't blink. I've checked fuses but nothing is blown
Thanks - SKI

 

check wiring

 

I had a very similar issue after accidentally drilling through a wire. It was the ground wire for the rear turn signal in the passenger side trunk tunnel. Have you done any work on the car recently? Might be worth looking at the wires in those areas.