Rear blinker bulb

Remove the rear passenger light assembly and inspect it. You may notice burned plastic in the connectors, which will explain the problem with bulbs not working.

The burned connectors are causing high resistance and when the headlights are on, there isn't enough current left to power the headlights and rear lights.

If the connectors are burned (usually the female connectors connected to the light assembly), you can lookup that part at Autozone or Rockauto. They may have "high temperature" sockets that you can swap out, so they can handle better current than the stock sockets, and you won't have to keep replacing the part.

There should two separate bulbs for marker and blinker. It sounds like a bulb is burnt out, bad ground, melted socket or a wiring anomaly. Are you certain it's supposed to have 57 series dual element bulbs for blinker and markers?

Could be a bad earth connection. What happens then is. The directional blinker uses the positive of the other one as an earth. When it happens again. Put your foot lightly on the brake pedal. And check if the blinking speed changes.

Burnt Out Lamp/Bulb--front or rear on right side

You have a broken Ground wire From Body to Frame . You Should Have a Heavy Braided Ground wire From Engine Block to Frame on Pass side, Then You will have another one that goes from firewall to engine , like at the back of the Head on passenger side to a screw to firewall.,....One of these is Broken,Loose, Corroded.

I would change out the dim bulb. usually blinkers blink when you have a bulb out either in the back or front blinker.if both are good then I would replace the flasher.

You have a bad connection at the rear passenger side turn signal. It is either the connection is corroded or a wire is loose on the ground side of the circuit.

Replace your "flasher relay, also know as a "blinker relay".Your local auto part store should carry them.

if you turn your blinker for passenger side on and if it blinks faster than normally you have a blown bulb

remove the trim panel at the very rear of trunk, remove it and place it out of the way, remove tail light Assembly retaining nuts top and bottom, I think there are 6 per side, pull the tail light assembly straight back to access the bulbs for replacement.