Opps I did not read your post correctly the first time. I had the same problem. If you have 12 volts at the socket you need to replace it with a 12 VOLT BULB. This is NOT a nornal house hold bulb which is 120 volts. It is a 12 volt light bulb that looks like a "normal" house hold light bulb but only works on 12 volts. I know this because I have an outdoor pole lamp fixture that is 12 volts. Years ago I tried a normal household bulb & it did not work. You have to get a 12 volt bulb.

Now where to get a 12 volt bulb can be easy or hard. My Home Depot & local large electrial supply did not carry them. Look at an RV motor home vender, ebay or Walmart in the RV section. I live in NJ & my local Walmart did not carry the 12 volt bulbs. When I was in Nebraska I stopped at Walmat at the RV section of the store. I then carried my 12 volt bulb (normal looking) back to New Jersery.