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:tu. Nice job and you even stuck with porcelain.

Trust me I've been an electrician for near 20 years, you seriously need to replace that thing.
Google search keyless light socket with pull chain, many direct replacements out there.

Day light LEDs from the orange box store the blue box store has them as well.
They come in many different styles standard bulb shape,candle,globe etc.
I changed out the whole house and saved about...