Daylight I think is enough. Milk frog doesn't move in the morning so I won't change it. but I don't see almost the vivarium in the darkness hours. I guess if I buy 50W I will see well the frog moving .
Well if you want to see the frog at night; just replace the moonlight with a red bulb of 15 or 25 watts. The higher watt moonlight could reverse your temperature gradient to point where night is warmer than cooler.
Remember to take care of the enclosure and it will take care of your frog !