Turn signals acting weird

I noticed last week that my turn signals were acting strange, so I replaced the signal flasher. It seemed to help for a while, but now they are acting strange again. When I turn on the signal, the signal starts flashing really fast like it's on speed or something. I have a 68 Valiant slant 6 with no mods to it or the electrical. Could it possibly be one of the bulbs is burning out or something? Seems to be for both left and right turn signal. Or should i look into pulling the steering wheel to check the turn signal mechanism?