I live in an older house and I have a two-socket light fixture in my bedroom. One socket will work with both an LED bulb and a basic (wire??) bulb. The other socket, however, only works with the basic bulb. Why is this and how can I fix it?
With the power off, try tugging gently at the pad in the middle of the socket well. You want it to be sprung a little further out. (Needle nose pliers can be useful for this.) There's a strong chance that it is pushed in a little too far to make contact with the tail of the bulb. If you pull it too much and it breaks, get another fixture.