Turn signal works but running light doesn't

[structured]

The other day I noticed that my right front running light is out.
I took out the bulb and noticed that it isn't blown but there is some evidence of water infiltration. Then I check my turn signals and they work. The bulb and connector can't be blown if the signals work. What else could it be?

[dgdavidson]

Running light = park light?

The wire going to the park light could be open, check that wire which (ETM 6314-0) is GY/WT and goes to pin 3 of the RH FRONT TURN/PARK LIGHT. GY/YL on the left side.

[structured]

running light = amber light is usually on when the headlights are on.

same light as turn signal. the problem is that it works as a turn signal, but doesn't go on like the other one when my headlights are on.