Riding fixed gear is like driving without brake lights

What if the brake switch broke? Or there is a fault in the wiring.

I remember a friend saying that they'd had a very confusing journey in a car where they kept finding themselves almost rear-ending the same Alfa-Romeo and it took them ages to work out that it was because its brake lights weren't working.

But- that's because people are lazy and look for visual cues that they expect to see: no brake lights, no slowing happening.

So yeah, this basically. I think the system that Jaguar developed (it could well be someone else) put the brake lights on if the driver lifted their foot quickly off the throttle i.e., something that indicated a rapid deceleration rather than just a moderation of speed.

I would not expect non-cyclists to pay any attention to a cyclists leg-speed in order to judge speed.
Generally not, but there have been quite a few comments about pedestrians being particularly cautious about stepping out in front of fixies, even if they are slowing, because it still looks like they're putting effort into keeping the bike going.