Will lightning make your vehicle headlights turn on?

You don't need proof IMHO. When lightning actually strikes something the effects are rather dramatic.

This is why you need to PHYSICALLY UNPLUG sensitive electronics. That or have a master disconnect switch on the NEUTRAL entrance feeder to your home or rig. A strike on nearby earth can travel to grounded electronics and jump to neutral and find a path through the circuitry. Extremely high voltage has a mind of it's own.

Want an example?

Auto ignition coil. You don't need to touch coil negative (ground) to get a jolt. Now magnify that voltage by a factor of 100. Scary

This past Saturday we were sitting in my garage waiting for a storm to blow by. The lightning was very intense. It hit somewhere close by and turned on the light to my garage door opener. I have about 6 witnesses to prove it...

I'd think it could easily turn headlights on, particularly if it uses an electronic switch or controller.

Saw it trigger a commercial fireworks display. Got into their electronic control system.

Sounds like a real world application of a Tesla coil making my hair stand on end.

Check a millivolt meter with two six foot leads the next thunderstorm.

Had it open the garage door when I was in the garage.

Oh this should be entertaining

It'll make a fence glow, it'll make your lights come on. As a Child I spent much time at Grand Ma's on the mountain. It was humid, almost like being in a cloud. I went outside, for whatever reason and the fence near the well and the big walnut was glowing blue and flame like blue waves or static was all up and down the fence. I walked near it and as I was about to touch it or grab it, it raced off to my left on the fence and just about disappeared. Little blue flames or static was here and there on the joints where the wire was woven. I have walked across that piece of ground during storms and felt static or electricity fom my feet up. there were other times of ball lightning along that same fence and once when it came through the closed kitchen door and out the living room window and another time it rolled along the top of the fence and seemed to jump from it and make a lot of sparks and I don't remember what happened to it from there. Uncle's coal truck had the wiring burned up, from what they thought was lightning around those years, while sitting near there.
I'm sure they must have experienced some adventures from lightning. They always turned off the battery powered radio and would not go near the well, nor sit near the windows. Lightning is very powerful and I don't remember an exact story of turning on vehicle lights, right now, I'm sure it could. I know that you can string lights between electrical towers and they will glow to even full brightness depending on the length and of the string and power and number of wires above. I've diverged a bit. :)

It could have been a few thousand feet away and be able to affect that electronic equipment.

I did not think it actually hit the vehicle but it seemed to have come close to it somehow. I wonder how close it has to come for that to happen? My battery operated postal scale went haywire at the same time. The readings were all over the place.