My car is a '99 Buick LeSabre with 53,000 miles on it. It has a V6 engine also. I was wondering where the flashers are located. My car's hazards work fine, but the blinkers are no longer flashing. They turn on and just sit as a solid color on both sides. I read that it does that when a light has burned out, but I have checked all the signal lights and they look fine.
I was told that this could be a need to replace the flasher for the turning signals.
Not sure if you still need this information, but someone else may. There are black plastic sound insulators under the dash of this car. You'll need a 7mm socket or nut driver to take them off. You have to take the passenger side one off to get the driver one off easily. The flasher relay is clipped to the inside of the sound insulator on the driver's side.
Given the mileage though, this is probably not the problem. But if you want to try replacing it they are cheap.