66 dart electrical problems

Mmmm, check the 2 bulbs to be sure both are oriented properly in their sockets. And check to see if the pin that is receiving power is the SAME pin in both sockets. There are 2 filaments in the bulb, one fed from each pin and both going to ground.. a bad ground at the non-working socket will cause it to not work. (But the blinker would not work right either.)

Insert the bulbs properly and check the voltage at the pin on each while the bulbs are inserted; you could have a poor wire connection from the junction of the 2 parking light wires and going to the non-working light.

Did you swap the bulbs to see if the problem stays on the same side?

Find an owner's manual for the green light; does it say "TURN' in the lettering in the light? If so, I will guess it is the older style common turn indicator (one indicator that blinks for either side's blinker).