Our house came with two very nice (and presumably expensive) pendant lights above the kitchen island. Over the last month, both stopped working. At first I did the obvious thing and replaced the bulb, but that didn't work. Then I replaced the transformer. Still no good. So I realized I needed to troubleshoot a little more methodically, and I got my multimeter out. I've only taken one apart, but it appears to me that there's a break somewhere in the cable near the bulb end. If I wiggle the socket, I can get the meter to read continuity, but it's intermittent. So I'm thinking I need to replace that part. However, unless I'm missing something, it looks like the bulb socket itself is part of the cable. Photo:

Is this something I'm actually going to be able to replace without replacing the entire fixture? What exactly do I need to look/ask for? Anything else to try first?