In fact, the OBJ model is a car.
The front and rear lights among others are a single surface on which the texture DDS file that pisses me off is applied.
The NVIDIA Texture Tools actually helped me understand the composition of the DDS file: the 3 channels of the RGB layer and one alpha channel related to transparency I guess.
I tried to solve my problem by separating, editing and combining each of the layers with transparent, white or black backgrounds, in the TGA, PNG or JPG formats, and even a Cutout Opacity map, but the parts of the surface that should appear more or less transparent are still rendered black or white depending on the combinations.