Hi
Led's come in a variety of sizes and setups. Some have no series resistor, they will instantly self destruct if you apply over 3V to them. Others are set up for 110V applications. They will do nothing at
12V. Some (but not many) are set up for AC. Most are set up for DC. You need to get the + and the - right both on the LED and the supply.
Neon bulbs are a bit similar. If you have a socket set up for one, there will be a ballast resistor wired to it. Put in any other sort of bulb and it's not going to light up.
If you short the feed wires together and measure at the bulb socket you should get < 1 ohm resistance. Unshort the feed wires and measure again. You should get infinite ohms. Hook up the wall wart and you should see the "12V" at the socket. If all that works and nothing lights up, it's the bulb / LED.
Bob