The actual use-case for those is that you can see the brake lights coming on for not only the vehicle in front of you, but at least the one in front of that as well, since you can see through the passenger space of the car in front of you. So it's not just a psychological issue here, but an actual visibility issue.

The same thing applies to blinker lights on side-view mirrors. They are much more visible at wider angles.

Better known as the 'CHMSL' (Center High-Mounted Stop Lamps)

High-mounted brake lights had an effect for the first 5-10 years or so, while they were still a novelty. After that, the benefit disappeared.

And a source for that would be interesting, while it makes intuitive sense I'd love to see someone who tested that hypothesis rigorously.

I don't have a source for it, sorry. I was chatting to someone involved in car safety research around 10 years ago, so it'll have to be listed as 'anecdata'.