There are no rear running lights, they are turn signals only.
The turn signal switches on early models don't have the contacts to shut the running light off on the signalling side. That makes the turn signals less effsctive especially in the dark as they would only change brightness not flash entirely off.
But you can do anything of course. A single LED lamp can be different brightness for two sources with 2 resistors and 2 diodes, the signal power goes througha standard diode to the bulb; the diode voltage drop won't dim it much. The running light power - ignition power on a bike without the stock wiring - goes through another diode and a resistor (probably 100 to 200 ohms, but you'll need to experiment) that provides less power and a dimmer bulb. The diodes isolate the 2 power sources, without them you''l have a mess. Only high-wattage LED units (with a single 1 or 3 watt LED) will have a problem with this dimming approach, they usually have a power regulator unit that will attempt to control the LED brightness over voltage fluctuations. I tried to make a simple schematic but my computer freehand drawing is double plus ungood.
The flasher suggestion has a problem in that many places ban non-red tail lights: only turn signals can be amber and must not stay on. Plus standard flashers power the lights through the turn signal switch, there's no "normally on" function. Paying a relative fortune for a "LED flasher" is silly when there are plenty of perfectly functional standard 3-terminal automotive flashers available MUCH cheaper.