Right Running Light & Turn Signal

I just bought a used 94 Grand Am. The right turn signal indicator on the dash remains on steady when the running lights or the headlights are on. Neither right side running light illuminates on the outside of the car. (There is a lamp near the radiator and one next to the headlight) The bulbs are ok. The lights do flash though when the turn signal is actually turned on. The left side of the car works normally. Any ideas about this problem? Thank You!

Have a 95 that had the same problem turned out to be the multifunction switch.

I had the same problem on my 88, and it turned out to be the light socket in the bumper was bad. The one wire broke causing it not to light but leaving the dash light on.