To relate a similar experience and my (in progress) solution: I noticed the high beam indicator stopped working. Since I recently replaced all the bulbs, that seemed odd. So, off the instrument cluster came (again): I have become very proficient at removing the instrument cluster lately.
Upon removal of the back covers and looking at the bulb terminals, everything appeared OK. But, after figuring out the contacts, testing with a multimeter showed no conduct at the high beam. I also noticed the neutral indicator light stopped working. That seemed odd too.
After some head scratching and close examination, the light bulb plugs had some corrosion. The mylar film copper contacts also had some corrosion. As it turns out, when the bulbs were replaced some dielectric grease should have been used to prevent corrosion. At least, that is my latest theory on how I screwed that up.
So, eventually, I got the high beam working again but the neutral light was stubborn. Fortunately, not as stubborn as me. It turns out the copper coating conductor was completely corroded (or abraded by me) away once the contact was clean. Oh, that is bad.
The first thing I tried was some silver paint. It did not work. The second was using some thin copper foil 1/4" wide and essentially replacing the copper foil for the bulb holder. A small (#49) drill was used by hand to make a hole in the copper foil which was then slid over the pin. The foil was long enough to lay over the damaged part and allow the bulb connector to make contact. It turned out (even though I could not really see this) that same replacement foil was needed for the other neutral light contractor pin.
I added some silver paint to the pins where the foil was laid - and got my neutral light working. I also used some Barges contact cement (the kind with toluene) to glue back some of the mylar that separated. Even though the silver paint did not fix the contact, it was added to all the other bulb connector foil parts - it seemed like the thing to do at the time.
With all the above, I was still not so happy about the fix. Really, some solder is needed between the pin and foil instead of the paint. So, upon doing an internet search, it turns out the mylar can be soldered with 63/37 tin-lead solder if done *very carefully*. For reasons I have simply accepted, I tend to get compulsive obsessive about things like this - they bother me.
As such, soldering the pins is the next step. Here is the McMaster part number for the foil I used: 76555A711, which has a conductive adhesive - but the adhesive did not really stick for me. I expect some heavy duty aluminum foil would work as well, but be harder to (eventually) solder. I also intend to try another type of silver paint. But, ultimately, I think that *careful* soldering is the ultimate fix. I also put dielectric grease on all the bulb holder contacts - which I think would have prevented this fiasco when the bulbs were changed in the first place.