I doubt that turn signal switch is causing this trouble. From what you said about the problem it would seem that the left side turn signals have a lower resistance (making the lights blink faster than normal) than the right side. @texases makes a good point about possibly having a bulb with the incorrect wattage installed. As a test, you could try removing both of the rear lights and then see how the blinkers react to that. If there is no change then do the same with the front lights.
Some blinkers use a thermally operated gadget, heats up, temperature rise due to current flow causes the light switch to turn off, temperature then falls, switch turns back on again, etc etc. Sort of a thermal oscillator. If there’s higher than normal resistance anywhere in the circuit it will still oscillate on and off, but slower.