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2008 F250
drove this am to work. left AND right directionals were blinking fast like a bulb is out.
no tail lights when head lights are on (left AND right)
no brake lights when head lights are on
with head lights off everything works
That definitely sounds like a grounding problem at the rear of the truck. Hopefully you have the EVTM manual for your truck. That will show where the grounds are for the tail lamp assemblies. On my 2003, both tail lamp assemblies (stop/turn/tail/backup) share ground #G400, which on my truck is located on the left frame rail near the rear wheel. I have heard that on later trucks (maybe yours), G400 is located on the frame crossmember above the spare tire. Let us know what you find.
Definitely sounds like a ground issue, I had an old chevy short box that wouldn't shut off when parked if you put trans in reverse with your foot on the brakes. It was back feeding through the accessory circuits and feeding the ignition because the box had lost it's ground.