Ford F-150 (2009-2014) :: 2011 - Turns Over But Doesn't Actually Start Sometimes

My Dad's 2011 Raptor has been having starting issues for about a month now. He turns the key, it turns over, but doesn't actually start; the same thing happens if he tries to start using remote start. It will start once in awhile on a 2nd or 3rd try, after throwing the shifter back and forth from Drive through Reverse several times and trying again, but not most of the time.

It doesn't happen all the time, but every once in awhile, and always at random times.

The first time was accelerating at an intersection a month ago. A second or so after hitting the gas, the engine died in the middle of the intersection. He took the key out, threw the shifter back and forth, tried again, and it started right up without issues.

Later that night, he tried starting it after sitting for over an hour (and had started it several times before without problems), and it failed to start, even after 7 or 8 tries. He had it towed to the dealer the next morning. He even tried starting it that morning in the dealer parking lot, without success. Several technicians apparently started it several times later that day without any issues! They didn't fix or replace anything, because they didn't find any problems. When he got it back, it worked perfectly.

A couple weeks later, it had the same problem at the gas station, after getting a full tank. My Mom told him that her truck (a nearly identical '11 Raptor) had the exact same issues several times in the past, and her trick was to let all the lights in the truck turn off, then try starting. He did that, and it worked!

Tonight, the same issue emerged. He did everything that had 'worked' in the past, and it still failed to start after about 10 tries. It's headed to the dealer on Monday, but what it might be?!? I also want to add that when it starts, it starts flawlessly, without hesitation; as if there wasn't a problem.