You might have a short. You would need to take you car in to a shop to find they short. They can be very difficult to locate.
Left and right stopped working? Check the fuse and/or the flasher relay. Only the left or the right stopped working? Check the bulbs.
No it means you have your left blinker on. The right bulbs have nothing to do with the left blinker. An incandescent bulb either works or it doesn't. There is no dying out.
Check to make sure all bulbs are working properly
If it is not blinking at all or blinks too fast, one of the bulbs is burned out.
Probably just a burned out bulb in the front one. Those bulbs have 2 elements so the marker light will still work but the blinker wont.
I had this same problem with my 1994 Town Car. After closely looking (the third time) at all the lamps I finally found one that wasn't working. I found it by turning on the hazards. The tail lights have two bulbs, top and bottom. It isn't obvious that one is out when you just turn the blinker on and look, but if you turn on the hazard flashers you can compare left and right to make sure that both sides are balanced. If that doesn't do it, it could still be the flasher relay module, other bulbs, or the switch on the column. But be sure to check ALL the bulbs first. The Town Car has about 4 bulbs on each side which flash with the blinker.
may be the connector that the bulb plugs into
Check if the alternator's working.
burnt light bulbs
Replace the signal flasher relay assuming you have physically seen front and rear, left and right signal bulbs flash.
open the rear doors or tail gate, there are two screws in the door jamb that hold the tail light lense in place, remove them and the lense will come off, there are 2 screws on the back of the lense that hold the assembly where the bulbs plug in, replace bulb and reversre to re-install
Left blinker= [Right blinker= ]