My car's right turn signal would work sometimes and other times it would not work even after I replaced the bulb.
My mechanic suggested I check the light socket and I found it was corroded and the bulb was loose when I inserted it.
I cleaned it with WD40 and took a very small screw driver and pryed the contacts together just a little bit. Make sure the power is off of course.
Since then the light has worked every time.