I need an LED to go in this base (the bulb on the right):

So I was looking at one of the white LEDS on this page:

http://www.superbrightleds.com/leds/w5_specs.htm

I think it would fit in the base, but would that one single LED light work with 12 volts? Or is there something else involved.

 

Hooking a single LED up to 12 volts will blow it all to hell. Quickly.
Using a single white LED, you would need to use a 560 ohm resistor in series with either lead. A red one would require 680 ohms.
Just be aware that those LED's have a relativley narrow beam to them; this particular one is 45° which is large for an LED. You may end up needing several to flood the area with light; this would require a different resistor value, which you can figure out by using this calculator http://www.hioutput.com/tech/circuits/resistance.html
Use a figure of 14.7 for automotive circuits, as that is close to what is in the system when charging.

 

Thanks. Its still new to me. Not sure what I am doing when I have to do it manually.