I've seen flashing third brake lights too.

I don't get adding flashing lights to brake and tail lights. It's actually worse, flashing lights make it harder for us to judge distance as now there's no steady queue needed for depth perception. It's why when cycling I've always opted for a solid taillight instead of the flashing ones.

Flashing third brake light (in the US) is usually a dealer profit addon. Personally, I think these violate federal vehicle safety law. I'll add a link to a federal letter that I think agrees with me [1]... But no enforcement means dealers alter the wiring harness to add these on to all their inventory and add a line item on the bill. They'll remove it if you complain, but the wiring harness has been altered.

I'm ok with factory strobing on hard braking, and I think that is permitted generally.

[1] https://www.nhtsa.gov/interpretations/20288ztv

I’ve seen a few cars that have strobe-then-solid brake lights from the factory, where the strobe only fires under hard deceleration. That seems like a safety win to me. (Remember it being on a high-spec Mercedes SL, and I’m pretty sure it was stock; looked it up and Mercedes calls it part of “Adaptive Braking”.)