Sounds like one cord is for the
pc lights and the other is for the moon lights. Have you tried just plugging the
pc cord into the timer and leave the moon light plugged directly into the wall? It also sounds like the moon lights are on all the time (since you didn’t mention a switch for them) which shouldn’t affect your display and since they are led lights you shouldn’t have to ever replace them.
If you plug just one or the other cords with both switches on do the moon lights come on? If so then you can just put the other cord on the timer to turn your
pc lighting on and off. I cycle mine from 9am to 9pm. If the moon lights are hardwired to only come on when the other two are off then it doesn’t sound like you will be able to use a timer and will just have to do it manually
The day/Actinic/moon lights are there to help simulate a full 24 hour lighting cycle. For example the actinic lights are used to simulate a morning/dusk type of light while the day would be on for around 6 hours to simulate daylight hours ie: from around 11am to 4pm. Lastly the moon lights are obviously designed to simulate moon light. (not trying to be smart, just fully explaining the purpose to those that might not understand)
Having said all that it really just depends on how you want to do it. If you are keeping corals than having just the actinic on during the day may not give them enough light but would be fine for a
fo setup while having just the day or both of them on shouldn’t hurt inverts or fish.