Testing your render engine I created a scene with two area lights. One behind the other. I wanted to see if the backlight also illuminated the scene without being obstructed by the light in front. And it didn’t happen.
It would be good if the lights had opacity and thus let the light that is behind pass through but still illuminating or affecting the reflection. In some cases I use a light for reflection and another for diffusion and then I have more control of the lighting.
Or sometimes if I use a texturedome and add an area light with a texture such as a circular gradient from white to black. In the reflection, in this case, you will see a square with the gradient from white to black (the area light) and then the texturedome. It would be good if only the illuminated part of the textured area light was then visible in the reflection. As if the area light were part of the texturedome. Without seeing the full shape of the area light.