Lights out for hair algae will not likely make a difference. Hair algae is the result of excess nutrients and/or inadequate flow in that area. Inadequate flow allows waste/nutrients to collect in that area instead of staying in the water column for removal. Step one is physical removal of as much of the hair algae as possible. Increase flow to that area if possible, either by redirecting your water flow or removing/adjusting anything that might be blocking the flow. Also, cut back on your feeding or, if you feel you've cut back all you can, feed the same amount in smaller more frequent feedings so it gets eaten quicker. Most people over feed, even if they think they don't.
Note that I'm assuming you are keeping your filter material clean, your skimmer working at peak efficiency, doing regular water changes, and using RO/DI water that you know has essentially zero TDS. Don't assume it's zero TDS, measure to make sure.
Carbon and GFO in a reactor are also very effective at removing nutrients. Also having a macro algae such as chaeto in a reverse cycle will help.
In simple terms, you have to get the nutrients out of the water such that the hair algae can't survive. Also note that hair algae doesn't die overnight. It can take several weeks to get it to go away.
Gary