Chaeto doesn't need a 24/7 light cycle. It doesn't hurt it to have it but it doesn't have to have it. The more light helps feed it with nutrients. Chaeto can actually survive with very small wattage of light. 24/7 lighting actually became more popular with caulpera. Its because it grows so quickly and eats up so much nutients out of the water that it can over clean the water of the nutrients that it needs to be fed. If it doesn't get enough to "eat" it could go asexual and that can ruin your whole tank. By keeping the lights on all the time it feeds the caulpera with all the nutrients that it needs. The chaeto is much slower growing and feeding and doesn't prevent the problem of going asexual. The time that the lights are out allows it to feed more on the phosphates and nitrates in the tank water. When the lights are on it's still feeding on these but it feeds more from the light provided. It will grow quicker with the lights on all the time helping to equal out the benifits of both situations. Don't worry it will survive in your tank.