Led and basic light bulbs; 2 light sockets. One works with both bulbs, the other doesn't.
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.