then all you'd really need to do is put the mirror in geosynch. Except for very brief periods around the spring and fall equinoxes, objects out at geosynch are in daylight 24 hours a day. The longest eclipse is on each equinox, and if the mirror is at zero degrees inclination, it only lasts for about 72 minutes. In the weeks immediately preceeding and following an equinox, the daily blackout goes from a few minutes gradually up to the max then tapers back down to nothing. In satellite operations, we referred to this as eclipse season.

However, I don't think the amount of light you'd get from such a mirror would amount to very much energy on the ground unless the mirror was enormous. A mirror that large would be difficult to launch and deploy. It'd also be tricky to maintain in position. Objects in geosynch orbit tend to drift due to irregularities in the Earth's gravity (caused by triaxuality points) and have to be nudged with thrusters every few weeks to keep in position. It'd also be damned by astronomers as a source of light pollution.