Chaeto uses both nitrate and phosphate, so it depends on your nutrients, most people add a gfo when their nitrate decreases but phospates are still high.
For lighting you could do with those reptile clamp fixtures, or Home Depot has them too, and a 5500k bulb. A outlet timer and have it running 18 hours on over night preferably .
But Chaeto is just one of the solutions, cause it would solve your future algae problems, and you would need to keep nitrates down either way for your corals so it's why I brought it up.
I use an algae scrubber and love it, but not many do these days, you could also do biopellets, there's many options.