I had a similar problem a couple of years ago where the right front turn signal would not blink, it would stay on solid and the directional arrow in the speedometer cluster would just stay on. Had good ground to the light reflectors on the factory setup but the plug connection for that light had some corrosion inside the male/female plug. Cleaned it up and applied some dielectric grease to the internals of the plug and it started working again as needed. Pic below is view of said plug.
Also note, the electrical function for the turn signal lights act a little different when headlights are both on and off. When the headlights are off, both the front signals and side marker lamps will blink at the same time. When the headlights are on, the front signals will blink alternately from the side markers. Meaning, front blinker on, side marker off. Front blinker off, side marker light on.