These lights:- ..... have a supercapacitor inside them, and they charge up in less than a minute from a dynamo, and run for 10 minutes or so after the bike stops. The light doesn't seem to dim when the bike stops, as long as it has run for a minutes or so before. When left for a long time, the light slowly fades out over several minutes.
The corresponding front light:- ..... also stays on when stationary, but dims when the bike stops. It seems to have two brightness levels, and I guess that the lower brightness when stopped is done to make the supercapacitor last longer.