An old friend of the Nelsons' writes:
Hey Paul, do you know a source for the bulb that actually goes inside a C7 bubble light? They appear to have a longer than normal shank on the threads than your typical C& type bulb. I have some Westinghouse indicator bulbs whose globe is similar in size but the threads are too short to make good contact.
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It's great to hear from you. Hope all is well.
I understand your problem; I don't think you're the only fellow who has encountered it. Some folks add a dab of solder to the tip of the base, but I'm not sure I would do that myself.
My friend Fred Fox who has a vintage Christmas store on Etsy (Noellkat) knows a lot more about most of this stuff than I do, so I'm going to copy this to him.
Also another friend Mark Podmore has had luck relamping these and written about it.
Fred and Mark, Tom gave me one of the archive copies of the OldChristmasLights web page, so he's one of the folks responsible for the Nelsons' information still being online. Hope you can help him.
Best of luck, - Paul