Kondo insulators and in particular their non-cubic representatives have remained poorly understood. Here we report on the development of an anisotropic energy pseudogap in the tetragonal compound CeRu$_4$Sn$_6$ employing optical reflectivity measurem
ents in broad frequency and temperature ranges, and local density approximation plus dynamical mean field theory calculations. The calculations provide evidence for a Kondo insulator-like response within the $a-a$ plane and a more metallic response along the c axis and qualitatively reproduce the experimental observations, helping to identify their origin.
