I figured out some more info. With the engine off, the headlights and secondary lights on and the fan on, when I activate the turn signal the radio will stay off. It won't flash and power on and off and on and off. It just stayed completely powered down. Even the power light goes off.

Could this be the alternator? Maybe it's not charging the battery like it should.

 

I tested the battery with the engine on and off. It seems to be good. I turned on as much as I can inside the cab (lights, alternate lights, fan, turn signal, etc...) and the multimeter dropped by 3 volts down to about 10 (if my meter was right)

My question is why would it only do this for a single turn signal and not both hazard lights?