I was in the same boat as you when I bought my house...
Since you got a good test result with a VOM, The only ideas I've got are.

Did you get the wrong size base when you bought a replacement bulb?

There may be something causing a short when you actually put the bulb in the socket.

The metal inside the socket might have corroded causing the bulb to not make good contact. This could be caused by a deposit, or the metal contact being completely corroded away at just the wrong spots. Here's a high res pic of what mine looked like. Since the socket was old and breaking apart, you can see inside it. There are springs that cause the contacts to touch the bulb. If those have corroded away that could cause this problem. https://secure.flickr.com/photos/148...33168/sizes/o/



I replaced the socket on a similar pool light once before. Got it from 1000bulbs dot com for about 3 bucks. I'm sure there's many more places you can order such a socket cheap. In the end I never was able to get the thing to stop leaking so I replaced the whole thing (that's an expensive way to go).