The problem was with the instrument illumination control unit or solid state controller (don't know the exact name for it) located right behind the instrument cluster. What happened was that the circuit in the illumination control unit got burned and shorted input wire (from the fuse box) with output wire (to interior lights) after I shorted some wires behind the radio. That's why I had my interior lights on all the time.
I'm attaching the instrument panel wiring diagram for 87 560sel.
May be itíll help somebody in the future.
It definitely helped me!
By the way, if you are going my way expect raining weather-wise.