With key in Accessory, the run circuit can be eliminated. Dana's tested that here 67-69 Dart Ignition Switch Pinout
But it makes sense. Otherwise why have an accsory postion on the switch.
Since it doesn't happen with the key off, that eliminates the main circuits that are always hot.
Besides the turn signal flasher, on the switched accessory circuit there's the wiper switch, and from the fuse box the heater blower, and radio circuits.