Easier than this... Connect the LED + wire to a constant power source, the - one to a switched one (acc, ignition whatever). You will find both in your car radio harness, or at the ignition switch. Yes the resistor in series is important.
In the past I wasn't a fan of those LED holder (call it whatever you want). In fact I can't remember having installing any. Instead I was just drilling a clean hole (usually with a UniBit step drill bit), then mount the LED behind. This allow to adjust the depth or mount it flush. You can use hot glue to secure it at the end.