LED bulbs are also diodes so they cause problems when installed into the side marker circuit which requires the bulb conduct current equally in both directions. LED bulbs only conduct in one direction. The current flow through the side marker circuit reverses when the headlights are turned on/off.
The suggested EP26-LED flasher won't help since it's purpose is to slow down the hyper-flashing speed that LED turn signal bulbs can cause.
Reversing the wiring to an LED side marker bulb can help it work better when the headlights are either on or off but not in both conditions.
If you are dead set on using LED bulbs in the side marker locations, the only real fix is to install a bridge rectifier onto both sides. That will allow the current to flow both directions through it while powering the LED bulb with the correct polarity so it works properly with the headlights on and off.