First you need to remove just the gauge cluster. On the W123 this can be done just by pushing on it from behind. Gain access by removing the knee pad dash cover (underside of dash on the drivers side). Push out to gain access to disconnet the wires and whatnot that run to the gauge clusster. Then there is like 6 or 7 screws to disassemble the gauge cluster from the back side. The section with the oil pressure, temp and fuel level is the only one with printed circuits, but you need to remove all the sections to get to it. Once apart look for the burnt spots.

Pretty simple once you look at it.

Glenn

Edit: Just reread your post. The console (portion of the dash that runs between the seats) doesn't need to come out to check the circuit boards. If you are looking to check the wiring under the console, remove the ashtray and the 2 screw behind it that hold the support bracket. Then remove the rubber ring from the gear selector. The carefully pry up the plastic top cover piece for the console while sliding it towards the rear of the car. The electrical connections to the window switches and hazards will have to be unplugged before it can be take totally off.