Just to put some numbers on it, GEO doesn't intersect the Sun-Earth line most of the time. The Earth's shadow touches GEO for a couple of weeks around the equinoxes, resulting in up to 70 minutes of shadow per day in that period. The rest of the time, they're in sun 100% of the time. So, as low as a 95% duty cycle at the worst point in the year, and 100% for most of the year.
The Earth will occasionally put such a satellite into shadow, but remember that the Earth is tilted, and so is the equator.
Getting up to GEO is hella expensive.