Great question! You can actually cause harm if you were to install a refugium at the "wrong time", but thankfully, it's pretty easy to tell when is the right/wrong time!
A refugium (I know you're talking about the light, but I'll just say refugium) is a great means of nutrient export (nitrate/phosphate). Therefore, if those levels are acceptable to you, you can actually do more harm by bottoming them out and starving your corals or inviting dinos! However, if you start to see those levels rising and your other nutrient export methods (water changes, skimmer, etc.) can't keep up, it's time to install the refugium! You might have to play with it a bit- you can set the light schedule to fine tune your nutrient levels- if they keep going down, reduce the photoperiod on your refugium light- if they keep rising, add a few more hours. The key here is to keep testing.
If you don't have access to any test kits, you can always go by the presence of hair algae and other less desirable organisms associated with high nutients. This is less precise and you may overshoot one way or another, but it's still a method none the less.
Ultimately, the easiest way to tell when to turn the light on and how long to run it would be to perform consistent testing (usually nitrate is enough). Once you hit the nitrate level you want and it's stable, you won't have to fiddle with your light anymore and you can simply harvest your cheato (or other macro algae) the same way someone would empty their skimmer cup.
As far as macro algaes are concerned, each grows slightly better in each tank. There isn't one right or wrong answer. Cheato is the most common as it seems to grow fastest in most tanks, however this isn't always the case. You might have to play around with what performs best in your particular environment (species differ in growth rate based on available nutrient levels and trace elements).
Another note, some people will still run a refugium for the effect on pH. If that's the case, you can start running it whenever, but it's very important to test your nutrient levels if that's your primary goal. In some cases, you might have to dose nitrate/phosphate to keep your levels up.
One last note: All the above information is to convey the idea that a refugium is not a "necessary" piece of equipment- it's simply an effective tool. Some tanks may never need a refugium for nutrient export, so it's always important to select your tools wisely

. It would be analogous to the question of whether someone needs a skimmer on a nano tank. Usually water changes alone will cover nutrient export , but it depends on each ecosystem and the nutrient levels

. If you do need to use that particular tool, it's a great tool!