We need to be a little more specific for the case where any tail lights don't work, because Hans und Fritz have played a little joke in there for us.
Start with the easy things... is the fuse okay, is the light bulb good. Use your tester to check whether power is getting to the socket.
Then comes the joke part. The tail lights on each side have a common ground "bus bar", a thin bit of brass(?) about 1/4 inch wide that bridges all the sockets. But it's held on with steel rivets, and over time Monsieur Galvan does his thing, and the electrical bond between the steel rivets and brass bar is no workie.
At this point one may utter some pithy comment as to the charm and quirkiness of old cars, or take to stronger language. Once past that, one can individually rig a ground for each socket, or if really, ahem, attentive, drill out the steel rivets and replace with brass. Or you can do something else. Lotsa luck.