It very easy to blow the fuse when testing a 12v socket with meter probes. The ground probe is fine as you do not need to insert it very far into the socket if at all. the positive probe must be inserted all the way in the socket to the very center without letting the probe touch the inner sidewall of the socket or you will blow the fuse. To avoid this, place an insulating tube over the positive probe leaving about 1/8 of an inch of the probe exposed at the very tip. This avoids the possibility of a short. I use a piece of shrink tubing which fits quite nicely. Some meters come with a protective add on for this purpose.
If you are sure you have found the correct fuse, take a look inside of the socket to see if it looks clean. I have found some sockets that have spun in the mounting hole causing the wires to be strained or fall off. Most wires attach via plugs. I have also found the plugs off of good mounted sockets. 9 out of 10 times the problem will be the fuse.