When I have the head lights on I lose my left tail light, turning light and the stop
light. When I turn off the head lights the left tail light works, the brake light and
I am having a very similar issue with my 2010 Ram 1500 ST 3.7L V6 single cab. When my head lights on, my rear left lights up bright solid, cannot see when I use signal. When head lights off, my front right signal lights up when I tap my break. I have not found the solution yet but if you do please let me know, you can email me to firstname.lastname@example.org. I can respond to you there if I find a solution before you do as well. Thanks.
It almost sounds like a ground is missing. Two filament bulbs have a common ground. If the ground is missing because of a broken wire or corrosion the current flows in on one filament to the base then out the other filament to another bulb on the same circuit to use it's ground.
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