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That sounds like a textbook loss of ground issue. Try running a temporary large gauge wire [10] from the negative post to the truck body and see if the problem goes away. Also follow the main ground cable to the engine block and inspect/tighten that connection. I've also encountered the situation where the cable looks good but has corroded inside the eye or terminal end fitting.
About 25 years ago I had a 72 Monte Carlo that developed an electrical issue. Everything was OK until the headlights were turned on. At this point the gas gauge went to empty, the turn signal arrows lit up and the high beam indicator worker backwards. In this case the dash panel had lost ground and a wire to the firewall fixed it.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.