Let me bounce this off you:

When I hook it up to DIS, I can activate each of the lights in the car individually (left low beam, right high beam, left fog light, right brake light, etc). When I perform that test, the lights work perfectly every time. The problem also doesn't change if I swap the entire lights side to side.

If the problem is with the module in the light itself (or the bulb or the igniter), the light wouldn't work during the test, correct? But it does. So that makes me think the problem is not with the actual headlight.

Plus there's this: 3E LCM: Fault, ALC control unit

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2002 X5 4.6is - Imola Red/Black (Sold)
2001 740i M Sport - Anthrazit Metallic/Black (Sold)
1998 M3/4/5 - Technoviolet/Dove (Sold)
2003 Z4 3.0i Sport - Sterlinggrau Metallic/Black (Sold)
2009 Mini JCW (The Wife's)
2015 i3 REx - Arravani Gray/Tera World (Daily Driver)