After reading your post again, I have to say that I'm 99% sure you need to replace the multifunction switch (which is the whole turn signal stick including the part that attaches to the steering column). You'll be taking the plastic off the steering column and the ingition key solenoid to remove it, but no big deal at all if you follow Haynes/Chilton.
Now that I think of it, even your local ford dealer should have the part for a price near what Mustangs Unlimited sells them for.
Your description is exactly the problem I had AND I too changed a couple bulbs that didn't need replacing.
Someone please speak up if I'm off here, but that's how I solved the problem.
Good luck.