Matt,
Check your grounds. Lots of the older cars used plug in sockets with the socket to hole friction fit to the body being the only ground. Over time rust & corrosion can build up in the groove on the socket, or on the sheet metal the socket plugs into. An easy test would to hook up a long jumper wire (small is OK) to your negative battery post, and then touch the other end to the light socket of the bulb not working to see if it lights. My old '60 Chevy (3 lights each side) used to get into some really funky blink patterns because of ground problems, and sneak circuits when it "hunted" for a missing ground.