I have volt meter that will show 12 volts is flowing. IE 2 probes, one on the live wire, and one on the other return cable on the connector. If you are getting 12v across the 2 wires that the bulb has plugged into it, then it shows that 12v is getting to the bulb, and then its the connector into the bulb is defective. You say you are getting 12 v but the electricity has to flow back too.
You can also put one probe end onto the live, and another to the earth of the car, and that should show 12v on the probe too
Probably making this sound way more complicated than it is
Its the return path, or the connector lampholder which the bulb fits into, or the bulb