Turn signal problem with 83 Impala???

I have a new to me 1983 Chevrolet Impala that is actually pretty new, 37,500 miles with 3.8L V6. The car is perfect except the turn signal is very slow and does not work at all when the headlights are on. I replaced the flasher with no success all is the same. All the lamps around the car work as they should including the headlights. I am new to Chevrolets so I don't have a clue.
Thanks,
David