I think that probably depends on the year of the vehicle.
My wife got in an accident with our 93 chevy G20 conversion van. When we got it back from the body shop, the anti-lock brake warning light was on, and half the dashboard lights were hanging under the dash. The force of the impact knocked them out of their sockets, and the ABS system got damaged. The insurance company refused to fix the anti-lock brakes. They said the impact of the accident could not have caused it, and the guy actually said he thought I was trying to get them to pay for something that was broken before the accident. I assured him I was not. He said he'd been investigating accidents with this specific vehicle for years, he's an expert on the subject, and could pull the data logging computer from the van and prove that the ABS system was broken before hand and I'm not telling the truth. I told him to go ahead and do it. He came back saying it would cost something like $800 to do that and they weren't going to pay for it. So I came back and said tell you what, you pull it and analyze it. If it shows I'm lying, I'll pay for the diagnostics. If it doesn't, you'll fix the brakes. He told me I'd be sorry.
Called me back an hour later and said that year van doesn't have a data logging computer. Unfortunately, that's when I said something about him being a %^&$@#!!! expert, yeah buddy. Well, they never paid for the ABS. And as soon as the accident cleared off the insurance I dumped them. My agent asked why, and I told him it was for several reasons. 1, my agent never went to bat for me. 2. I don't like being called a liar by a liar. 3. KMA and another choice acronym.
I got another ABS module from the junkyard and repaired it myself for a couple hundred.
Anyhow, data logging doesn't exist on many older cars.
I don't know if they could tell from burnt filaments if your brake lights were on or not when you go hit. That would be an interesting subject to discuss.
I'd heard about this years ago, and am finally learning not to make a statement on TBN which I can't back up.
From this site Vehicle Inspection and Analysis an explanation of how/why they can tell.
Turn signals, headlights and brake lights can be examined to determine whether or not they were on or off during the car crash.
The filaments within the light bulb get extremely hot when on and are cold when off.
Since the filament is very thin, significant impacts to a vehicle can often cause these filaments to deform greatly and get tangled up.
This phenomenon is called hot shock.
If a great enough impact occurs and the filament is cold, a phenomenon known as cold shock can occur. This looks significantly different in that the filament is usually the same shape as an intact filament but broken. No significant deformation or tangling occurs. Other considerations must be taken into account when analyzing these bulbs, but these are the most basic two situations.