69 valiant electrical gremlin turn signal and license plate light

Make SURE you have the correct / compatible bulb. License lamp should be single contact

Both these sound like ground problems. The lic. lamp branches off from the tail light harness so first thing is make sure it is getting power. Make sure your test light is grounding. I use places like the trunk latch.

To test that a socket such as a parking light is grounding, think what happens.........the light gets power to the center pin, the current path is lamp bulb shell............to socket shell..........to ground.

If that path is broken, then wherever that break "is" the point will "at 12V" because the current has no where to go

So with lights on, and make sure that the lamp you are testing does have power on the wire, and that the bulb is good, Make certain your lamp is grounding, then probe the socket shell itself. Wiggle the bulb. If you get any glimmer of light while probing the socket shell, the socket is not grounding

Maybe the shell is grounding but the connection between bulb shell and socket is poort. With some lamp/ sockets, you can carefully probe and make contact on the bayonet pins. If you get a light there and not off the socket, then the bulb is simply not making contact with the socket.