Of course when the engine isn't running and the blinkers are flashing faster, you have the key in the on position. Correct?
How is the four way blinker? Do the exhibit the same thing with the engine running compared to it off? Also which speed seems more normal to you? The engine off or the engine on?
Back in the day, I had an old Oldsmobile. When a bulb died, they would blink slow. That was in the 80s, I'm sure the circuit is different on current cars.
When the key in "on" but engine not running both the left & right turn signals and the four-way's work properly. All bulbs are working. Engine running, headlights "on" turn signals operate significantly slower than with key "on", engine off. C