Dashboard backlight stopped working

[Fujikama]

Hey guys,

I tried to repair the speedometer, and I did achieve success*, yet the backlight stopped working. And I have no idea how it happened. Worse, I don't have any more ideas about how to repair it.

At first, the right bulb stopped working. I thought, "Okay, I short-circuited, or else. I will replace it, and it will be fine."
I replaced the right side one... and both stopped working. What the heck?
I've checked the fuses (5, 6, and 9) by swapping them (with 2). Everything is fine, all of them are intact. So there was no short-circuit in the first place, it seems.
I've also checked the dimmer, but it doesn't affect dead-dark bulbs in any way. The rest of the instruments dim/light up correctly.

The car is '83 BMW 518 (without i), European version with VDO instrument cluster. Images below. Bulbs have Ga RAY, not brown case.
 

* Removed the corroded VARTA batteries, and did a bypass as described in this thread: viewtopic.php?t=94937. 12V+ bypass was enough. Didn't need to do all 3 of them.

[Blue Shadow]

Check to see if you get voltage in the circuit. Bad, dirty bulb holders, missing ground connection. 

you do have the wiring diagrams, don’t you?  

The ETM is for US cars but dash lights would be something that is the same. There are also € wiring diagrams. 

[Aldo525]

Check again the right position/contact of both bulb sockets between the socket and circuit plate. Reconnect the cluster, lights on and move the sockets clockwise and counterclockwise and you will realise the bad connection. 

[Philo]

My tach light goes out some times.  If I pound on top of the dash it comes back on.  My light sockets are either corroded of lose.  

[Shawn D.]

You've already gotten good advice on the technical aspect, but I'll help you with the linguistic aspect:  E28s do not have a "backlight" for the cluster.  The light does not come from behind the gauges, it is shone onto the front of the gauges.  It's simply "gauge lighting," not "gauge backlighting."

FWIW, this error is committed by folks whose first language is English, so I expect it's picked up from them by those whose first language is not English.

[Philo]

Classic Shawn..,  but he's right