Light is not going to cause wort to go skunky, but can cause this problem with beer. This is because the light wavelengths that cause beer to skunk fall between about 350 and 550 nanometers; 350 nm is the upper end of the ultraviolet range (invisible to the human eye) and 550 nm is in the visible range. These wavelengths are associated with purple, blue, and green colors (I will get back to this later). We all know that sunlight causes beer to go skunky, and most of us have probably experienced a non-skunky beer transform into a skunk cloud on a sunny day. As far as normal light (the sorts of lights we are exposed to on a regular basis) goes, sun is the gold medal winner for skunking beer. German steins with lids were supposedly designed to prevent debris from old roofs and ceilings from falling into beer, but these lids may have also been useful for preventing skunkiness . . . antique sunglasses for beer!
Incandescent and halogen lights emit a broad spectrum of light wavelengths and are generally accepted as the most natural looking because this broad range is similar to sunlight. While these lights do emit wavelengths that cause beer to skunk, the light color is skewed toward the longer wavelengths (yellow, orange, red, and burgundy colors) that do not cause this reaction. Unlike sunlight — and incandescent and halogen bulbs — LED and fluorescent lights emit more specific wavelengths. As it turns out, most LED and all fluorescent lights both have major peaks around 400 nm. What this means to the beer lover is that LED and fluorescent lights are more apt to cause beer to go skunky than incandescent and halogen lights.
There are a few things that can be done to minimize skunkiness in the homebrewery, however. Glass carboys have many positive attributes, but the two major pitfalls are their relative fragility, and their clear nature. If you ferment and age your homebrew in glass, be careful to avoid exposure to sunlight, as well as LED and fluorescent bulbs. You should also minimize exposure to incandescent and halogen lights, but these lights do not cause most beers to go skunky. It is easy enough to cover a carboy with a towel or light blanket if you do not have space in a dark closet to shield your beer from light, and this may be something you want to do.
Stainless steel containers totally block light, so if you use stainless fermenters there are no worries. Plastics range from opaque to clear, so, depending on the plastic, light may or may not pass into your beer.
Beer color and glass color also relate to this topic. Dark beers absorb a broader spectrum of light wavelengths than lighter colored beers, so as beer becomes lighter in color, the propensity for skunkiness goes up. The same sort of thing happens with glass bottle color; brown glass absorbs the blue, purple, and green wavelengths that catalyze the skunk reaction, whereas clear, green, and blue glass all allow some, or all in case of clear bottles, of these wavelengths into the beer.
As with any chemical reaction, the rate of a reaction increases with the concentration of the participants, and also increases with the concentration of catalysts. Light is a catalyst in the skunk reaction; if light in the 350–550 nm is exposed to prone beer (anything other than black beers or beers with light stable hop compounds), the beer will eventually become skunky. Time is the part of your question that I cannot answer, but the preventative measures are pretty simple to follow. Hope this helps you in your quest for great beer!