Iguanas really don't need any lighting at night. That being said, the lights from heating pads, power strips, electrical outlet plug-in night lights, and diffuse moonlight (or a street lamp) are acceptable and may in fact help them in case they are startled awake. Many an iguana owner has been awakened at night by the sounds of thrashing preceded or followed by a thud, the unmistakable sound of an iguana body hitting a hard surface at some velocity. Iguanas, like other animals, may be disoriented if they are startled awake for some reason.
Iguanas usually need heating at night, though the nighttime temperatures are not as high as they are during the day. Because we cannot use white or other bright lighting at night due to how they disrupt the iguana's sleep function, we need to use sources of heat that produce no light or dim light. What you end up using will depend upon whether or not your iguana is free roaming or enclosed, the availability of multiple sleeping areas arrayed across a vertical and horizontal gradients, the time of year, and how the room and enclosure temperatures are affected by outside temperatures. You may need to use one or more heating devices in order to attain and maintain the nighttime thermal gradient iguanas require.
A space heater and lots of sleeping area options work for some iguanas. An infrared heating device, such as a ceramic heating element (CHE) or infrared panel, neither of which produce any visible light, may be best for enclosed iguana. Another option is a light bulb made specifically for nocturnal reptiles; they produce a very dim purplish light generally well tolerated by diurnal reptiles at night. Some people are able to find opaque red, green or blue incandescent light bulbs at regular lighting stores. These also produce very dim light.
If you do find these opaque bulbs or try a nocturnal bulb, you will need to try the different colors out to see which, if any, your iguana tolerates the best. Some do fine under the green or blue but not the red, for example. Signs of disturbance may include increased restlessness at night; drop in appetite; sluggishness during the day; crankiness; and other signs of being "out of sorts". These signs may take several days or even weeks to become apparent, so keep watching for such changes after you install one of these bulbs.
What about if you are using the same room at night for activities that require light? A little low ambient room lighting is probably okay (there have been no longitudinal studies on this aspect of their health at this point). Anything more than that should be avoided. That means if your iguana in a room where you normally have a bright light on until 10 PM or so, either the light or the iguana needs to move. Turning off the lights but having the television on can also be disturbing as the eyes and parietal eye detect the flickering light even when the iguana is resting with his eyes closed or is asleep.
If your iguana is housed in an enclosure, you may be able to cover the front and sides of the enclosure with an opaque, light-blocking fabric. This will enable you to have light on in that room. A dark fabric color blocks more light than a pale one.
Remember to make sure that any such cover is safe: if the iguana's heat lamp comes into close contact (or proximity) with the fabric cover, the fabric may catch on fire. The same is true if the fabric cover is close to the daytime lights. If you oversleep and don't get the cover removed before the automated daytime lights come on, you could be in for a rude awakening.
Fire safety can't be stressed enough when it comes to any pet, but is of special concern when it comes to reptiles in general, and iguanas in particular, because of all the heating and lighting equipment they require. There have been far more home and school fires caused by iguanas actively trying to break out of their enclosures or knocking over poorly mounted, easily accessible light fixtures than fires caused by the activities of other reptiles.