Upon examining the alpha channel of the image (which I should have done in the first place), I see that the area light is, in fact, not black, but simply not present. The space in which the light should be has a completely transparent (black) spot in the alpha channel. The light itself works fine, but simply creates a black spot in the alpha channel, displaying whatever background color I have set for the camera behind it in the color image. Again, this only happens when I set the area light to quote-unquote "visible." So, as a correction to my original question, how do I prevent the area light from having this "black hole" effect in my image?