3rd gen T/A, turn signal trouble???

I have a '84 Pontiac Trans Am V8 (L69) 305 High Output, automatic transmission. My turn signal issue is when a turn on the car and try the right turn signal it won't flash outside. When I have the headlights on at night the right turn signal does the same with the addition of the turn signal display on the dash being constantly ON. When I signal to the LEFT it works just fine. I checked the front right parking and turn signal bulbs, but the are OK. Next to check would be the flasher under the dash or the turn signal switch in the steering column. Can someone shed some light on this issue??? Thank you. :cool:

If the dash indicator comes on and stays solid, that means a bulb is out, probably the rear since the front checks out.