I have seen two types of lamps on the old cast iron machines, slight variations on them, but construction wise much the same.
One type is a large lupmy looking lamp with a thick glass lens you pull off when you replace the bulb, it's often the internal copper parts that's been damaged. It has an on/off switch you turn clock wise and if someone has forced it the other way parts likely have broken. I tried to fix this once, but I had never seen the internals of it before, and I eneded up buying a replacement part on the web (used Singer lamp missing the glass lens). If you are handy with tiny parts made of thin copper plates you can make new connector spring. I didn't understand what was wrong until I had all the fully working switch parts in front of me so I never attempted it. I imagine it's not easy to get the parts bended the right way, I assume the original parts where pressed into shaped in a special mould.
The other type lamp; slender and a bit longer, with out any glass lens, just a semi covering shade made of bakelite and a metal lining between the bulb and the bakelite parts. Older 15Ks might have a shiny all metal of the same construciton. This type of lamp tend to be intact and working, since the switch can't be fored the wrong way (it's either left or right position). With this type I would inspect the copper connecting parts and check if they are clean and not broken. There is a metal bit in there that acts like a spring.
Last edited by Mickey2; 10-20-2015 at 02:23 AM.