Those third brake lights have a strobe module installed. They flash several times to get your attention, then go solid. Pretty neat idea. I would definitely consider adding one of those! Here is an example on YouTube.
[LINK]You can buy them on eBay, Amazon on many other vendors. Google “third brake light strobe”.
I think that is the ideal solution, that is if there is an actual solution to the problem (since it requires the person behind you to actually be looking ahead at the road).
A friend in Florida was rear ended in his 1935 Cadillac just a couple months after he finished restoration. He had a third brake light mounted on the license plate above the rear mount tire.
It made no difference, of course, since the nitwit that hit him was texting on her phone instead of looking at the brake lights.