I have a 94 FLSTC and have changed things, switch is like old style ignition first then lights. I have added LEDS and a trailer converter to allow the rear turn signals to be run/brake/turn. Everything was working just great until I had to have shoulder surgery back in April. That meant the scooter sat idle. Even though I kept a battery maintainer on it the battery died (5 years old so I wasn't surprised) Now with a new battery the brake & turn works fine until I turn on the headlights then everything blinks no matter which turn signal. I suspect a pinched wire but can't find one. All bulbs are working, the problem only happens when running lights are on and I use either turn signal.
Any help is appreciated

 

I would jump the trailer converter out and check it. All it is is one way diodes. I grabbed a cheap set of trailer lights for my boat trailer and one of the wires inside was crimped to the metal bracket that went to ground and it took the convert and shorted it together and let current go both ways across one diode. Cost me $50.00 using a $20 set of trailer lights. Those converts will not take much load. Not sure if you have added resistors with the LED like my 04 would need. I have the Harley plug and play converter but it's just a fancy trailer converter. Back in 83 on a Toyota, I made one with some diodes from Radio Shack

 

I have even changed the converter (had a new one for spare)
I can try just eliminating it. I used front turn signals on the rear to give me dual filament. Like I said until I turn on the headlight/running lights it works great.
The last time I had a problem it was a shorted resistor, so I relocated them. I really like having the LEDs they are bright.