I do not intend to sound pompous, but we seem to be overthinking the solution. Are we not?

EpicDesyre pretty much fixed his with a simple solution.

I fixed mine with an even simpler solution.
The issue to this problem is: Over a period of time, the socket contact loses electrical connection to the bulb. The bulb is not the issue.

The bad contact is easily identified by looking at the one with soot, corrosion and maybe even physical wear. Mine had a small hole at the contact point.

I simply sanded the soot and corrosion with 200 grit sandpaper, used an old toothbrush to remove the dust then used a jewelers flathead screwdriver to pry up the contact about 2mm, then protected the metal with fish oil as an anti-corrosion protectant using a small cotton swab. Finished it by re-assembling everything back to normal.