I have a 2000 Dodge Ram 2500 with a plow mount. When I turn on my right turn signal, without the headlights on, the radio lights blink with the turn signal. When the headlights are on, right turn signal does not work. (left one seems to work fine.)

Any thoughts?

Thanks

 

It sounds like a bad ground condition with the RS signal. I assume you have a plow setup with lights and directionals on it. If the ground is bad the current will seek out any place it can find to create a circuit. In this case it looks like it picked your radio light. When your headlights are on the normal current flow from the dashlights opposes the current flow from the signal seeking a ground point.
1- Operate your emergency lashers and see what happens when all signal lights should be flashing. What is the radio light doing then?
2- Isolate the plow wiring from the rest of your harness and see what happens with the signals.
3- If the problem disappears withe plow rig disconnected secure a better ground source for the wiring and reconnect the plow rig and re-test.

If this doesn't help list what you have done and what other symptoms you have and I might be able to supply a better solution.