I don't use a submersible light, I use a CF bulb on a clip-on fixture. I have more room to work with because I have a sump/fuge plumbed below my tank. the light does not need to be submersible that was just an example. you can also do a 'soap-dish' method where the chaeto is in the display and uses the display lights. you could definitely work out some way to mod a bulb into your rear chamber, it'll be better to ask someone with a nano cube about that.
This guy did a mod for growing chaeto in the back chamber but i didn't see exactly what he did. This lighting question would be better answered by another nanocube owner. I do encourage you to ask, there are a good amount on NR.
As to the lunar lights, they do not contribute much to a tank IMO. I use my lunars on a timer to simulate a natural light cycle. Mine are a spotlight type array of RB LEDs. they turn on 1.5 hrs before my actinics, they then shut off 15 min after the actinics are on. About an hour later my MH turns on and runs for 8 hrs. my actinics stay on 1.5 hrs after the MH shuts off, and then the lunars go on, 15 min later my actinics are off. The lunars stay on till about midnight, so maybe 2 hrs.
Jstvd8, your tang may have just been stressed from the move, and the lunars may have had nothing to do with it. As I said earlier they are primarily aesthetic, I wouldn't run them all night though because organisms that only come out after dark won't be going to lighted parts of the tank. this is however just my opinion.