how long to keep lights on

I try roughly to imitate the season. On when the sun is rising out at dusk.

 

The lights stay on for 12 hours but ..... From January to Juni I increase the period with half an hour every month. From July to December I decrase this period by half an hour every month. So the period in December is 12 hours and in July the period is 15 hours. By this I follow the season in my part of the world.

 

Just a word of advice: assuming the trash can lid is intended to be a reflector to redirect the "wasted" light to the plant, it's shiny nature is actually defeating that to a significant degree.

Both of the light sources are beaming nearly parallel to the lid. That means that most of the reflected light will be equally reflected, nearly parallel to it, away from the plant. The fact that it's not totally polished to a mirror finish means some is dispersed more broadly, but very little. If you were to put a matte white board (poster board or foamcore would be good) behind each lamp, perpendicular to the beam on the opposite side, you'd get a significantly better result.