Fog Light Wiring Question

I like the simplicity of the guide in this write up:
http://www.naxja.org/forum/showthread.php?t=1013846

however i want to make sure i build that jumper right.

is that 16/18 gauge wire(does it really matter)?

and whats the technical name of those two metal pieces being held on by the heat shrink/solder slugs

they look like small battery terminals

I would use 14 AWG for my own amusement, although 16 should be fine as well. 18 is getting a bit small, but that's a very short piece.
The terminals (also called connectors, and quick disconnects, among other things) are called "male spades". Available just about everywhere. Those are crimped on, btw. That's just the plastic insulation the 14-16 AWG connectors use. The 18-20 AWG connectors have red insulation, typically.
Example
http://www.dormanproducts.com/dorman/p-12559-85453.aspx